diff --git a/CHANGELOG.md b/CHANGELOG.md
index 47a207c4f9c51fe97700b83a711c40e17581a9db..26f0e8b84520743c2dd84d24bad37e33e66e2f46 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,13 @@
+v1.0.0
+------
+* Removed the `simulator/ravaflow24` module.
+
+* Replaced deprecated `scipy.interpolate.interp2d` with `scipy.interpolate.RegularGridInterpolator` to maintain compatibility with newer versions of SciPy.
+  
+* Added citation information to the README.
+
+* Added repeated k-fold validation for `emulator/robustgasp` module.
+
 v0.2.1
 ------
 * Set R_HOME automatically for conda environment to ensure seamless installation.
diff --git a/docs/source/_build/html/.buildinfo b/docs/source/_build/html/.buildinfo
index d675874cbdd48dacee0caa6e36af7a14806a9066..0a18d44599e1a93b2d16688b2ae8d69212b3c3da 100644
--- a/docs/source/_build/html/.buildinfo
+++ b/docs/source/_build/html/.buildinfo
@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 9b954c6b6aa24d57cc63cce736384000
+config: 2b3fc487307e1c52bb522fa4713f5ca7
 tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/docs/source/_build/html/.doctrees/changelog.doctree b/docs/source/_build/html/.doctrees/changelog.doctree
index 51352fbd09747dbcc5e6c5ce01f9f1de23faa8b2..2d0925187eb5c99dfefc48947f4f296df615e363 100644
Binary files a/docs/source/_build/html/.doctrees/changelog.doctree and b/docs/source/_build/html/.doctrees/changelog.doctree differ
diff --git a/docs/source/_build/html/.doctrees/emulator/robustgasp.doctree b/docs/source/_build/html/.doctrees/emulator/robustgasp.doctree
index 8e8238f035110cc19c1d2f7bde806b87aac10057..7bc3460a8a37516ad14f4635c6cf3e832d1178d6 100644
Binary files a/docs/source/_build/html/.doctrees/emulator/robustgasp.doctree and b/docs/source/_build/html/.doctrees/emulator/robustgasp.doctree differ
diff --git a/docs/source/_build/html/.doctrees/environment.pickle b/docs/source/_build/html/.doctrees/environment.pickle
index 7426d03d2b1b439573ffd33523788c5bc0d3f07b..d0eefeec6e9f39e9c5a04c4d7dd15efad448393d 100644
Binary files a/docs/source/_build/html/.doctrees/environment.pickle and b/docs/source/_build/html/.doctrees/environment.pickle differ
diff --git a/docs/source/_build/html/.doctrees/index.doctree b/docs/source/_build/html/.doctrees/index.doctree
index f1675e9a8f10b9964b7f4ff603807cd9fa8b828a..413357e2662092150d2120b2160225fd68838b59 100644
Binary files a/docs/source/_build/html/.doctrees/index.doctree and b/docs/source/_build/html/.doctrees/index.doctree differ
diff --git a/docs/source/_build/html/_modules/index.html b/docs/source/_build/html/_modules/index.html
index d0368cb7da1a14c1edd7466b306e4ad55db3ef49..86bb9903727bf3ad90660cdc2170f7b1446fac96 100644
--- a/docs/source/_build/html/_modules/index.html
+++ b/docs/source/_build/html/_modules/index.html
@@ -99,7 +99,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/_modules/psimpy/emulator/robustgasp.html b/docs/source/_build/html/_modules/psimpy/emulator/robustgasp.html
index 8c4bfdaec7a26020a120f361f936f92e041304b4..b17a4b33c00dd00dd77ab6c663345130b33cfa55 100644
--- a/docs/source/_build/html/_modules/psimpy/emulator/robustgasp.html
+++ b/docs/source/_build/html/_modules/psimpy/emulator/robustgasp.html
@@ -15,12 +15,11 @@
     <script src="../../../_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="../../../" id="documentation_options" src="../../../_static/documentation_options.js"></script>
-        <script src="../../../_static/jquery.js"></script>
-        <script src="../../../_static/underscore.js"></script>
-        <script src="../../../_static/_sphinx_javascript_frameworks_compat.js"></script>
-        <script src="../../../_static/doctools.js"></script>
-        <script src="../../../_static/sphinx_highlight.js"></script>
+        <script src="../../../_static/jquery.js?v=5d32c60e"></script>
+        <script src="../../../_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="../../../_static/documentation_options.js?v=37f418d5"></script>
+        <script src="../../../_static/doctools.js?v=888ff710"></script>
+        <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/js/theme.js"></script>
     <link rel="index" title="Index" href="../../../genindex.html" />
     <link rel="search" title="Search" href="../../../search.html" /> 
@@ -31,14 +30,18 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="../../../index.html" class="icon icon-home"> psimpy
+
+          
+          
+          <a href="../../../index.html" class="icon icon-home">
+            psimpy
           </a>
               <div class="version">
-                0.1.2
+                0.2.1
               </div>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="../../../search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -66,7 +69,7 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="../../../index.html" class="icon icon-home"></a></li>
+      <li><a href="../../../index.html" class="icon icon-home" aria-label="Home"></a></li>
           <li class="breadcrumb-item"><a href="../../index.html">Module code</a></li>
       <li class="breadcrumb-item active">psimpy.emulator.robustgasp</li>
       <li class="wy-breadcrumbs-aside">
@@ -78,46 +81,68 @@
            <div itemprop="articleBody">
              
   <h1>Source code for psimpy.emulator.robustgasp</h1><div class="highlight"><pre>
-<span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span></span><span class="kn">import</span> <span class="nn">os</span>
+
+<span class="k">if</span> <span class="s2">&quot;CONDA_PREFIX&quot;</span> <span class="ow">in</span> <span class="n">os</span><span class="o">.</span><span class="n">environ</span> <span class="ow">and</span> <span class="s2">&quot;R_HOME&quot;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">os</span><span class="o">.</span><span class="n">environ</span><span class="p">:</span>
+    <span class="c1"># if a conda environment is active and the R_HOME variable was not set</span>
+    <span class="n">R_home</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s2">&quot;CONDA_PREFIX&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="s1">&#39;/lib/R&#39;</span>
+    <span class="k">if</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">R_home</span><span class="p">):</span>
+        <span class="n">os</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s1">&#39;R_HOME&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">R_home</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">from</span> <span class="nn">rpy2.robjects.packages</span> <span class="kn">import</span> <span class="n">importr</span>
 <span class="kn">import</span> <span class="nn">rpy2.robjects.numpy2ri</span>
 <span class="kn">from</span> <span class="nn">rpy2.rinterface</span> <span class="kn">import</span> <span class="n">NA</span>
 <span class="kn">from</span> <span class="nn">rpy2.rinterface_lib.sexp</span> <span class="kn">import</span> <span class="n">NALogicalType</span>
 <span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
 <span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">RepeatedKFold</span>
+<span class="kn">from</span> <span class="nn">contextlib</span> <span class="kn">import</span> <span class="n">nullcontext</span><span class="p">,</span> <span class="n">contextmanager</span>
+<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_absolute_percentage_error</span><span class="p">,</span> <span class="n">r2_score</span><span class="p">,</span> <span class="n">root_mean_squared_error</span>
+<span class="kn">import</span> <span class="nn">io</span>
+<span class="kn">import</span> <span class="nn">sys</span>
 
 <span class="n">rpy2</span><span class="o">.</span><span class="n">robjects</span><span class="o">.</span><span class="n">numpy2ri</span><span class="o">.</span><span class="n">activate</span><span class="p">()</span>
-<span class="n">RobustGaSP</span> <span class="o">=</span> <span class="n">importr</span><span class="p">(</span><span class="s1">&#39;RobustGaSP&#39;</span><span class="p">)</span>
+<span class="n">RobustGaSP</span> <span class="o">=</span> <span class="n">importr</span><span class="p">(</span><span class="s2">&quot;RobustGaSP&quot;</span><span class="p">)</span>
 
 <span class="c1"># fetch @</span>
 <span class="n">r_base</span> <span class="o">=</span> <span class="n">importr</span><span class="p">(</span><span class="s2">&quot;base&quot;</span><span class="p">)</span>
 <span class="n">r_at</span> <span class="o">=</span> <span class="n">r_base</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">[</span><span class="s2">&quot;@&quot;</span><span class="p">]</span>
 
-<span class="k">class</span> <span class="nc">RobustGaSPBase</span><span class="p">:</span>
 
+<span class="k">class</span> <span class="nc">RobustGaSPBase</span><span class="p">:</span>
     <span class="nd">@beartype</span>
     <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
-        <span class="bp">self</span><span class="p">,</span> <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">zero_mean</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;No&#39;</span><span class="p">,</span> <span class="n">nugget</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">ndim</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+        <span class="n">zero_mean</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;No&quot;</span><span class="p">,</span>
+        <span class="n">nugget</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span>
         <span class="n">nugget_est</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
-        <span class="n">range_par</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">NALogicalType</span><span class="p">]</span> <span class="o">=</span> <span class="n">NA</span><span class="p">,</span> 
-        <span class="n">method</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span><span class="s1">&#39;post_mode&#39;</span><span class="p">,</span> <span class="n">prior_choice</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;ref_approx&#39;</span><span class="p">,</span>
-        <span class="n">a</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.2</span><span class="p">,</span> <span class="n">b</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-        <span class="n">kernel_type</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;matern_5_2&#39;</span><span class="p">,</span>
-        <span class="n">isotropic</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span> <span class="n">optimization</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s1">&#39;lbfgs&#39;</span><span class="p">,</span>
-        <span class="n">alpha</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">lower_bound</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
-        <span class="n">max_eval</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">num_initial_values</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+        <span class="n">range_par</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">NALogicalType</span><span class="p">]</span> <span class="o">=</span> <span class="n">NA</span><span class="p">,</span>
+        <span class="n">method</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;post_mode&quot;</span><span class="p">,</span>
+        <span class="n">prior_choice</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;ref_approx&quot;</span><span class="p">,</span>
+        <span class="n">a</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.2</span><span class="p">,</span>
+        <span class="n">b</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">kernel_type</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;matern_5_2&quot;</span><span class="p">,</span>
+        <span class="n">isotropic</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+        <span class="n">optimization</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;lbfgs&quot;</span><span class="p">,</span>
+        <span class="n">alpha</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">lower_bound</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
+        <span class="n">max_eval</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">num_initial_values</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span><span class="p">,</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Set up basic parameters of the emulator.</span>
 
 <span class="sd">        Parameters</span>
 <span class="sd">        ----------</span>
 <span class="sd">        ndim : int</span>
 <span class="sd">            Input parameter dimension.</span>
-<span class="sd">        zero_mean : str, optional </span>
+<span class="sd">        zero_mean : str, optional</span>
 <span class="sd">            If `&#39;Yes&#39;`, the mean is set to zero. If `&#39;No&#39;`, the mean is</span>
 <span class="sd">            specified by ``trend``. Default is `&#39;No&#39;`.</span>
 <span class="sd">        nugget : float, optional</span>
-<span class="sd">            Nugget variance ratio. </span>
+<span class="sd">            Nugget variance ratio.</span>
 <span class="sd">            If :math:`0`, there is no nugget or the nugget is estimated.</span>
 <span class="sd">            If not :math:`0`, it means a fixed nugget. Default is :math:`0`.</span>
 <span class="sd">        nugget_est : bool, optional</span>
@@ -182,7 +207,7 @@
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span> <span class="o">=</span> <span class="n">ndim</span>
 
-        <span class="k">if</span> <span class="n">zero_mean</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;No&#39;</span><span class="p">,</span> <span class="s1">&#39;Yes&#39;</span><span class="p">]:</span>
+        <span class="k">if</span> <span class="n">zero_mean</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;No&quot;</span><span class="p">,</span> <span class="s2">&quot;Yes&quot;</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;zero_mean can be either &#39;No&#39; or &#39;Yes&#39;.&quot;</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span> <span class="o">=</span> <span class="n">zero_mean</span>
 
@@ -191,56 +216,56 @@
 
         <span class="k">if</span> <span class="n">range_par</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">NA</span><span class="p">:</span>
             <span class="k">if</span> <span class="n">range_par</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">1</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">range_par</span><span class="p">)</span> <span class="o">!=</span> <span class="n">ndim</span><span class="p">:</span>
-                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                    <span class="s2">&quot;range_par must be 1d numpy array of length ndim&quot;</span><span class="p">)</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;range_par must be 1d numpy array of length ndim&quot;</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">range_par</span> <span class="o">=</span> <span class="n">range_par</span>
 
-        <span class="k">if</span> <span class="n">method</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;post_mode&#39;</span><span class="p">,</span> <span class="s1">&#39;mmle&#39;</span><span class="p">,</span> <span class="s1">&#39;mle&#39;</span><span class="p">]:</span>
-            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                <span class="s2">&quot;method can only be &#39;post_mode&#39;, &#39;mmle&#39;, or &#39;mle&#39;.&quot;</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">method</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;post_mode&quot;</span><span class="p">,</span> <span class="s2">&quot;mmle&quot;</span><span class="p">,</span> <span class="s2">&quot;mle&quot;</span><span class="p">]:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;method can only be &#39;post_mode&#39;, &#39;mmle&#39;, or &#39;mle&#39;.&quot;</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="n">method</span>
 
-        <span class="k">if</span> <span class="n">prior_choice</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;ref_xi&#39;</span><span class="p">,</span> <span class="s1">&#39;ref_gamma&#39;</span><span class="p">,</span> <span class="s1">&#39;ref_approx&#39;</span><span class="p">]:</span>
+        <span class="k">if</span> <span class="n">prior_choice</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;ref_xi&quot;</span><span class="p">,</span> <span class="s2">&quot;ref_gamma&quot;</span><span class="p">,</span> <span class="s2">&quot;ref_approx&quot;</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                <span class="s2">&quot;prior_choice can only be &#39;ref_xi&#39;, &#39;ref_gamma&#39;,&quot;</span>
-                <span class="s2">&quot; or &#39;ref_approx&#39;.&quot;</span><span class="p">)</span>
+                <span class="s2">&quot;prior_choice can only be &#39;ref_xi&#39;, &#39;ref_gamma&#39;,&quot;</span> <span class="s2">&quot; or &#39;ref_approx&#39;.&quot;</span>
+            <span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span> <span class="o">=</span> <span class="n">prior_choice</span>
 
         <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">=</span> <span class="n">b</span>
 
-        <span class="k">if</span> <span class="n">kernel_type</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;matern_3_2&#39;</span><span class="p">,</span> <span class="s1">&#39;matern_5_2&#39;</span><span class="p">,</span> <span class="s1">&#39;pow_exp&#39;</span><span class="p">]:</span>
+        <span class="k">if</span> <span class="n">kernel_type</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;matern_3_2&quot;</span><span class="p">,</span> <span class="s2">&quot;matern_5_2&quot;</span><span class="p">,</span> <span class="s2">&quot;pow_exp&quot;</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                <span class="s2">&quot;kernel_type can only be &#39;matern_3_2&#39;, &#39;matern_5_2&#39;,&quot;</span>
-                <span class="s2">&quot; or &#39;pow_exp&#39;.&quot;</span><span class="p">)</span>
+                <span class="s2">&quot;kernel_type can only be &#39;matern_3_2&#39;, &#39;matern_5_2&#39;,&quot;</span> <span class="s2">&quot; or &#39;pow_exp&#39;.&quot;</span>
+            <span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">kernel_type</span> <span class="o">=</span> <span class="n">kernel_type</span>
 
         <span class="bp">self</span><span class="o">.</span><span class="n">isotropic</span> <span class="o">=</span> <span class="n">isotropic</span>
 
-        <span class="k">if</span> <span class="n">optimization</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;lbfgs&#39;</span><span class="p">,</span> <span class="s1">&#39;nelder-mead&#39;</span><span class="p">,</span> <span class="s1">&#39;brent&#39;</span><span class="p">]:</span>
+        <span class="k">if</span> <span class="n">optimization</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;lbfgs&quot;</span><span class="p">,</span> <span class="s2">&quot;nelder-mead&quot;</span><span class="p">,</span> <span class="s2">&quot;brent&quot;</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                <span class="s2">&quot;optimization can only be &#39;lbfgs&#39;, &#39;nelder-mead&#39;, or &#39;brent&#39;.&quot;</span><span class="p">)</span>
+                <span class="s2">&quot;optimization can only be &#39;lbfgs&#39;, &#39;nelder-mead&#39;, or &#39;brent&#39;.&quot;</span>
+            <span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">optimization</span> <span class="o">=</span> <span class="n">optimization</span>
 
         <span class="k">if</span> <span class="n">alpha</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             <span class="n">alpha</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">ndim</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1.9</span>
         <span class="k">elif</span> <span class="n">alpha</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">1</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">alpha</span><span class="p">)</span> <span class="o">!=</span> <span class="n">ndim</span><span class="p">:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;alpha must be 1d numpy array of length ndim&quot;</span><span class="p">)</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span> <span class="o">=</span> <span class="n">alpha</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span> <span class="o">=</span> <span class="n">alpha</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
 
         <span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span> <span class="o">=</span> <span class="n">lower_bound</span>
 
         <span class="k">if</span> <span class="n">max_eval</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-            <span class="n">max_eval</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="mi">30</span><span class="p">,</span> <span class="mi">20</span> <span class="o">+</span> <span class="mi">5</span><span class="o">*</span><span class="n">ndim</span><span class="p">))</span>
+            <span class="n">max_eval</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="mi">30</span><span class="p">,</span> <span class="mi">20</span> <span class="o">+</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">ndim</span><span class="p">))</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span> <span class="o">=</span> <span class="n">max_eval</span>
 
         <span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">num_initial_values</span><span class="p">)</span>
 
         <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="kc">None</span>
-    
-    <span class="k">def</span> <span class="nf">_preprocess_design_response_trend</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
-        <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">trend</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="nf">_preprocess_design_response_trend</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">trend</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Preprocess design, response, and trend before train an emulator.</span>
 
 <span class="sd">        Parameters</span>
@@ -266,20 +291,19 @@
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;design must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
         <span class="k">elif</span> <span class="n">design</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
             <span class="n">design</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">design</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">design</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
-        
+
         <span class="k">if</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;design must match the input dimension ndim&quot;</span><span class="p">)</span>
 
-        <span class="bp">self</span><span class="o">.</span><span class="n">design</span> <span class="o">=</span> <span class="n">design</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">design</span> <span class="o">=</span> <span class="n">design</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
 
         <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">response</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">response</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;response must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
         <span class="k">elif</span> <span class="n">response</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
             <span class="n">response</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">response</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">response</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
         <span class="k">if</span> <span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
-            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                <span class="s2">&quot;response must have same number of points as design&quot;</span><span class="p">)</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">response</span> <span class="o">=</span> <span class="n">response</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;response must have same number of points as design&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">response</span> <span class="o">=</span> <span class="n">response</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
 
         <span class="k">if</span> <span class="n">trend</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">))</span>
@@ -289,20 +313,22 @@
             <span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">trend</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">trend</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
         <span class="k">if</span> <span class="n">trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;trend must have same numer of points as design&quot;</span><span class="p">)</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">trend</span> <span class="o">=</span> <span class="n">trend</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">trend</span> <span class="o">=</span> <span class="n">trend</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span> <span class="o">==</span> <span class="s2">&quot;Yes&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
 
-        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span> <span class="o">==</span> <span class="s1">&#39;Yes&#39;</span><span class="p">:</span>
-            <span class="bp">self</span><span class="o">.</span><span class="n">trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
-        
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-            <span class="bp">self</span><span class="o">.</span><span class="n">_b</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> \
-                <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">+</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_b</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">**</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">+</span> <span class="n">design</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+            <span class="p">)</span>
         <span class="k">else</span><span class="p">:</span>
             <span class="bp">self</span><span class="o">.</span><span class="n">_b</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span>
 
-    <span class="k">def</span> <span class="nf">_preprocess_testing_input_trend</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
-        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+    <span class="k">def</span> <span class="nf">_preprocess_testing_input_trend</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Preprocess testing_input and testing_trend before make prediction or</span>
 <span class="sd">        draw samples.</span>
 
@@ -324,12 +350,11 @@
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;testing_input must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
         <span class="k">elif</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
             <span class="n">testing_input</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">testing_input</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
-        
+
         <span class="k">if</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ndim</span><span class="p">:</span>
-            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                <span class="s2">&quot;testing_input must match the input dimension ndim&quot;</span><span class="p">)</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;testing_input must match the input dimension ndim&quot;</span><span class="p">)</span>
 
-        <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span> <span class="o">=</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span> <span class="o">=</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
 
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span> <span class="o">==</span> <span class="s2">&quot;Yes&quot;</span><span class="p">:</span>
             <span class="n">testing_trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">))</span>
@@ -339,24 +364,45 @@
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;testing_trend must be 1d or 2d numpy array.&quot;</span><span class="p">)</span>
         <span class="k">elif</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
             <span class="n">testing_trend</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">testing_trend</span><span class="p">,</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">testing_trend</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
-        
-        <span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span> <span class="o">=</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span> <span class="o">=</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
 
         <span class="k">if</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
-                <span class="s2">&quot;testing_trend must have same numer of points as testing_input&quot;</span><span class="p">)</span>
+                <span class="s2">&quot;testing_trend must have same numer of points as testing_input&quot;</span>
+            <span class="p">)</span>
 
         <span class="k">if</span> <span class="n">testing_trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">trend</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
                 <span class="s2">&quot;testing_trend must have the same basis as the trend used&quot;</span>
-                <span class="s2">&quot; for emulator training.&quot;</span><span class="p">)</span>
+                <span class="s2">&quot; for emulator training.&quot;</span>
+            <span class="p">)</span>
+
+    <span class="nd">@contextmanager</span>
+    <span class="k">def</span> <span class="nf">_nostdout</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Discard any output to the standard output stream (stdout).</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">save_stdout</span> <span class="o">=</span> <span class="n">sys</span><span class="o">.</span><span class="n">stdout</span>
+        <span class="n">sys</span><span class="o">.</span><span class="n">stdout</span> <span class="o">=</span> <span class="n">io</span><span class="o">.</span><span class="n">StringIO</span><span class="p">()</span>
+        <span class="k">yield</span>
+        <span class="n">sys</span><span class="o">.</span><span class="n">stdout</span> <span class="o">=</span> <span class="n">save_stdout</span>
 
-<div class="viewcode-block" id="ScalarGaSP"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP">[docs]</a><span class="k">class</span> <span class="nc">ScalarGaSP</span><span class="p">(</span><span class="n">RobustGaSPBase</span><span class="p">):</span>
 
-<div class="viewcode-block" id="ScalarGaSP.train"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.train">[docs]</a>    <span class="nd">@beartype</span>
-    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
-        <span class="n">trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+<div class="viewcode-block" id="ScalarGaSP">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP">[docs]</a>
+<span class="k">class</span> <span class="nc">ScalarGaSP</span><span class="p">(</span><span class="n">RobustGaSPBase</span><span class="p">):</span>
+<div class="viewcode-block" id="ScalarGaSP.train">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.train">[docs]</a>
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+        <span class="n">verbose</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Train a scalar GP given training data.</span>
 
 <span class="sd">        Parameters</span>
@@ -374,36 +420,42 @@
 <span class="sd">            If `None`, a :code:`(ntrain, 1)` matrix of ones is used.</span>
 <span class="sd">            If :math:`q=1`, both :code:`(ntrain, 1)` and :code:`(ntrain,)`</span>
 <span class="sd">            :class:`numpy.ndarray` are valid.</span>
+<span class="sd">        verbose : bool, optional</span>
+<span class="sd">            If `&#39;True&#39;`, Displays detailed information.</span>
+<span class="sd">            Default is `True`.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_design_response_trend</span><span class="p">(</span><span class="n">design</span><span class="p">,</span> <span class="n">response</span><span class="p">,</span> <span class="n">trend</span><span class="p">)</span>
 
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
             <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;ScalarGaSP only works for scalar-output model&quot;</span><span class="p">)</span>
 
-        <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">rgasp</span><span class="p">(</span>
-            <span class="n">design</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">design</span><span class="p">,</span>
-            <span class="n">response</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="p">,</span>
-            <span class="n">trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">trend</span><span class="p">,</span>
-            <span class="n">zero_mean</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">zero_mean</span><span class="p">,</span>
-            <span class="n">nugget</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">nugget</span><span class="p">,</span>
-            <span class="n">nugget_est</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">nugget_est</span><span class="p">,</span>
-            <span class="n">range_par</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">range_par</span><span class="p">,</span>
-            <span class="n">method</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="p">,</span>
-            <span class="n">prior_choice</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span><span class="p">,</span>
-            <span class="n">a</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">,</span>
-            <span class="n">b</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_b</span><span class="p">,</span>
-            <span class="n">kernel_type</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">kernel_type</span><span class="p">,</span>
-            <span class="n">isotropic</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">isotropic</span><span class="p">,</span>
-            <span class="n">optimization</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">optimization</span><span class="p">,</span>
-            <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
-            <span class="n">lower_bound</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span><span class="p">,</span>
-            <span class="n">max_eval</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span><span class="p">,</span>
-            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">)</span></div>
-    
-<div class="viewcode-block" id="ScalarGaSP.predict"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.predict">[docs]</a>    <span class="nd">@beartype</span>
-    <span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
-        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+        <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nostdout</span><span class="p">()</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">verbose</span> <span class="k">else</span> <span class="n">nullcontext</span><span class="p">():</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">rgasp</span><span class="p">(</span>
+                <span class="n">design</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">design</span><span class="p">,</span>
+                <span class="n">response</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="p">,</span>
+                <span class="n">trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">trend</span><span class="p">,</span>
+                <span class="n">nugget</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">nugget</span><span class="p">,</span>
+                <span class="n">method</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="p">,</span>
+                <span class="n">prior_choice</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span><span class="p">,</span>
+                <span class="n">a</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">,</span>
+                <span class="n">b</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_b</span><span class="p">,</span>
+                <span class="n">kernel_type</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">kernel_type</span><span class="p">,</span>
+                <span class="n">isotropic</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">isotropic</span><span class="p">,</span>
+                <span class="n">optimization</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">optimization</span><span class="p">,</span>
+                <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
+                <span class="n">lower_bound</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span><span class="p">,</span>
+                <span class="n">max_eval</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span><span class="p">,</span>
+                <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">,</span>
+            <span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="ScalarGaSP.predict">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.predict">[docs]</a>
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">predict</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Make prediction using the trained scalar GP emulator.</span>
 
 <span class="sd">        Parameters</span>
@@ -425,7 +477,7 @@
 <span class="sd">            Emulator-prediction at ``testing_input``. Shape :code:`(ntest, 4)`.</span>
 <span class="sd">            `predictions[:, 0]` - mean,</span>
 <span class="sd">            `predictions[:, 1]` - low95,</span>
-<span class="sd">            `predictions[:, 2]` - upper95, </span>
+<span class="sd">            `predictions[:, 2]` - upper95,</span>
 <span class="sd">            `predictions[:, 3]` - sd</span>
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
@@ -438,15 +490,23 @@
             <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span>
             <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">,</span>
             <span class="n">interval_data</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-            <span class="n">outasS3</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+            <span class="n">outasS3</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="p">)</span>
         <span class="n">predictions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_predictions</span><span class="p">))</span>
 
         <span class="k">return</span> <span class="n">predictions</span></div>
 
-<div class="viewcode-block" id="ScalarGaSP.sample"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.sample">[docs]</a>    <span class="nd">@beartype</span>
-    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
-        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="ScalarGaSP.sample">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.sample">[docs]</a>
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
+        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Draw samples using the trained scalar GP emulator.</span>
 
 <span class="sd">        Parameters</span>
@@ -472,28 +532,32 @@
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
-        
+
         <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_testing_input_trend</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">)</span>
 
         <span class="n">r_samples</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">Sample</span><span class="p">(</span>
             <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span>
             <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span>
             <span class="n">num_sample</span><span class="o">=</span><span class="n">nsamples</span><span class="p">,</span>
-            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span>
+            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">,</span>
+        <span class="p">)</span>
         <span class="n">samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_samples</span><span class="p">)</span>
 
         <span class="k">return</span> <span class="n">samples</span></div>
 
-<div class="viewcode-block" id="ScalarGaSP.loo_validate"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.loo_validate">[docs]</a>    <span class="k">def</span> <span class="nf">loo_validate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="ScalarGaSP.loo_validate">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.ScalarGaSP.loo_validate">[docs]</a>
+    <span class="k">def</span> <span class="nf">loo_validate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Validate trained scalar GP emulator using leave-one-out-cross-validation.</span>
 
 <span class="sd">        Returns</span>
 <span class="sd">        -------</span>
 <span class="sd">        validation : numpy array</span>
 <span class="sd">            Shape :code:`(n, 2)`.</span>
-<span class="sd">            validation[:, 0] - leave one out fitted values,</span>
-<span class="sd">            validation[:, 1] - stand deviation of each prediction</span>
+<span class="sd">            validation[:, 0] - leave-one-out fitted values</span>
+<span class="sd">            validation[:, 1] - standard deviation of each prediction</span>
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
@@ -501,20 +565,88 @@
         <span class="n">r_validation</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">leave_one_out_rgasp</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">)</span>
         <span class="n">validation</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_validation</span><span class="p">))</span>
 
-        <span class="k">return</span> <span class="n">validation</span></div></div>
+        <span class="k">return</span> <span class="n">validation</span></div>
+
+    
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">repeated_kfold_validate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">k</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">5</span><span class="p">,</span> <span class="n">repeat</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">10</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">dict</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Performs repeated K-Fold cross-validation on trained emulator. Calculates</span>
+<span class="sd">        MAPE, NRMSE, and R^2 errors.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">            k : int, optional</span>
+<span class="sd">                K-factor. Default is :math:`5`.</span>
+<span class="sd">            repeat : int, optiona</span>
+<span class="sd">                Repeat-factor. Default is :math:`10`.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">            validation_dict : dict</span>
+<span class="sd">                A dictionary consists of key-value pairs of error metrics (MAPE, </span>
+<span class="sd">                NRMSE, and R^2) and numpy array of respective error per validation</span>
+<span class="sd">                step.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
+        
+        <span class="n">X</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">design</span>
+        <span class="n">y</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span>
+
+        <span class="n">rkf</span> <span class="o">=</span> <span class="n">RepeatedKFold</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">n_repeats</span><span class="o">=</span><span class="n">repeat</span><span class="p">)</span>
+        <span class="n">nval</span> <span class="o">=</span> <span class="n">rkf</span><span class="o">.</span><span class="n">get_n_splits</span><span class="p">()</span> 
+
+        <span class="n">MAPE</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">nval</span><span class="p">)</span>           <span class="c1"># mean absolute percentage</span>
+        <span class="n">R_squared</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">nval</span><span class="p">)</span>      <span class="c1"># coefficient of determination</span>
+        <span class="n">NRMSE</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">nval</span><span class="p">)</span>          <span class="c1"># normalized root mean square</span>
 
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="n">train_index</span><span class="p">,</span> <span class="n">test_index</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">rkf</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">X</span><span class="p">)):</span>
+            <span class="n">training_inputs</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">train_index</span><span class="p">,</span> <span class="p">:]</span>
+            <span class="n">training_outputs</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">train_index</span><span class="p">]</span>
+            <span class="n">testing_inputs</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">test_index</span><span class="p">,</span> <span class="p">:]</span>
+            <span class="n">testing_outputs</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">test_index</span><span class="p">]</span>
 
-<div class="viewcode-block" id="PPGaSP"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP">[docs]</a><span class="k">class</span> <span class="nc">PPGaSP</span><span class="p">(</span><span class="n">RobustGaSPBase</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">training_inputs</span><span class="p">,</span> <span class="n">training_outputs</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+            <span class="n">prediction</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">testing_inputs</span><span class="p">)[:,</span> <span class="mi">0</span><span class="p">]</span>
 
-<div class="viewcode-block" id="PPGaSP.train"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.train">[docs]</a>    <span class="nd">@beartype</span>
-    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
-        <span class="n">trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+            <span class="n">R_squared</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+            <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">prediction</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+                <span class="n">R_squared</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">r2_score</span><span class="p">(</span><span class="n">testing_outputs</span><span class="p">,</span> <span class="n">prediction</span><span class="p">)</span>
+
+            <span class="n">MAPE</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">100</span> <span class="o">*</span> <span class="n">mean_absolute_percentage_error</span><span class="p">(</span><span class="n">testing_outputs</span><span class="p">,</span> <span class="n">prediction</span><span class="p">)</span>
+
+            <span class="n">RMSD</span> <span class="o">=</span> <span class="n">root_mean_squared_error</span><span class="p">(</span><span class="n">testing_outputs</span><span class="p">,</span> <span class="n">prediction</span><span class="p">)</span>
+            <span class="n">mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">testing_outputs</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">mean</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">sys</span><span class="o">.</span><span class="n">float_info</span><span class="o">.</span><span class="n">epsilon</span><span class="p">:</span>
+                <span class="n">NRMSE</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">NRMSE</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span>  <span class="n">RMSD</span> <span class="o">/</span> <span class="n">mean</span>
+
+        <span class="n">validation_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;MAPE&quot;</span><span class="p">:</span> <span class="n">MAPE</span><span class="p">,</span> <span class="s2">&quot;NRMSE&quot;</span><span class="p">:</span> <span class="n">NRMSE</span><span class="p">,</span> <span class="s2">&quot;R_squared&quot;</span><span class="p">:</span> <span class="n">R_squared</span><span class="p">}</span>
+        <span class="k">return</span> <span class="n">validation_dict</span></div>
+
+
+
+<div class="viewcode-block" id="PPGaSP">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP">[docs]</a>
+<span class="k">class</span> <span class="nc">PPGaSP</span><span class="p">(</span><span class="n">RobustGaSPBase</span><span class="p">):</span>
+<div class="viewcode-block" id="PPGaSP.train">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.train">[docs]</a>
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">design</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">response</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Train a parallel partial GP given training data.</span>
 
 <span class="sd">        Parameters</span>
 <span class="sd">        ----------</span>
-<span class="sd">        design : numpy array </span>
+<span class="sd">        design : numpy array</span>
 <span class="sd">            Training input points. Shape :code:`(ntrain, ndim)`.</span>
 <span class="sd">            ``ntrain`` is the number of training points, ``ndim`` is the input</span>
 <span class="sd">            dimension. If :math:`ndim=1`, both :code:`(ndim, 1)` and</span>
@@ -533,8 +665,9 @@
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
             <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
                 <span class="s2">&quot;PPGaSP should be used for models with vector output.&quot;</span>
-                <span class="s2">&quot; For scalar output model, please use ScalarGaSP.&quot;</span><span class="p">)</span>
-        
+                <span class="s2">&quot; For scalar output model, please use ScalarGaSP.&quot;</span>
+            <span class="p">)</span>
+
         <span class="bp">self</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">ppgasp</span><span class="p">(</span>
             <span class="n">design</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">design</span><span class="p">,</span>
             <span class="n">response</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="p">,</span>
@@ -553,12 +686,17 @@
             <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
             <span class="n">lower_bound</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span><span class="p">,</span>
             <span class="n">max_eval</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span><span class="p">,</span>
-            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">)</span></div>
+            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">,</span>
+        <span class="p">)</span></div>
+
 
-<div class="viewcode-block" id="PPGaSP.predict"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.predict">[docs]</a>    <span class="nd">@beartype</span>
-    <span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
-        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+<div class="viewcode-block" id="PPGaSP.predict">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.predict">[docs]</a>
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">predict</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Make prediction using the trained parallel partial GP emulator.</span>
 
 <span class="sd">        Parameters</span>
@@ -594,7 +732,8 @@
             <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span>
             <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">,</span>
             <span class="n">interval_data</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-            <span class="n">outasS3</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+            <span class="n">outasS3</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="p">)</span>
 
         <span class="n">ntest</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
         <span class="n">nresponse</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
@@ -605,10 +744,17 @@
 
         <span class="k">return</span> <span class="n">predictions</span></div>
 
-<div class="viewcode-block" id="PPGaSP.sample"><a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.sample">[docs]</a>    <span class="nd">@beartype</span>
-    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
-        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="PPGaSP.sample">
+<a class="viewcode-back" href="../../../emulator/robustgasp.html#psimpy.emulator.robustgasp.PPGaSP.sample">[docs]</a>
+    <span class="nd">@beartype</span>
+    <span class="k">def</span> <span class="nf">sample</span><span class="p">(</span>
+        <span class="bp">self</span><span class="p">,</span>
+        <span class="n">testing_input</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span>
+        <span class="n">nsamples</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
+        <span class="n">testing_trend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Draw samples using the trained parallel partial GaSP emulator.</span>
 
 <span class="sd">        Parameters</span>
@@ -629,7 +775,7 @@
 <span class="sd">        Returns</span>
 <span class="sd">        -------</span>
 <span class="sd">        samples : numpy array</span>
-<span class="sd">            Shape :code:`(ntest, nresponse, nsamples)`. </span>
+<span class="sd">            Shape :code:`(ntest, nresponse, nsamples)`.</span>
 <span class="sd">            `samples[:, :, i]` corresponds to i-th realization of the trained</span>
 <span class="sd">            emulator at ``testing_input``, i=1, ..., ``nsamples``.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
@@ -637,16 +783,16 @@
             <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">&quot;Emulator has not been trained!&quot;</span><span class="p">)</span>
 
         <span class="bp">self</span><span class="o">.</span><span class="n">_preprocess_testing_input_trend</span><span class="p">(</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="p">)</span>
-        
+
         <span class="n">ntest</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
         <span class="n">nresponse</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">response</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
-        
+
         <span class="c1"># extract trained parameters of ppgasp_emulator</span>
         <span class="n">sigma2_hat</span> <span class="o">=</span> <span class="n">r_at</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span> <span class="s2">&quot;sigma2_hat&quot;</span><span class="p">)</span>
         <span class="n">nugget</span> <span class="o">=</span> <span class="n">r_at</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span> <span class="s2">&quot;nugget&quot;</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
         <span class="n">beta_hat</span> <span class="o">=</span> <span class="n">r_at</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emulator</span><span class="p">,</span> <span class="s2">&quot;beta_hat&quot;</span><span class="p">)</span>
-        <span class="n">range_par</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">beta_hat</span>
-        
+        <span class="n">range_par</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">beta_hat</span>
+
         <span class="c1"># set up a rgasp_emulator using trained parameters of ppgasp_emulator</span>
         <span class="n">rgasp_emulator</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">rgasp</span><span class="p">(</span>
             <span class="n">design</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">design</span><span class="p">,</span>
@@ -656,7 +802,7 @@
             <span class="n">nugget</span><span class="o">=</span><span class="n">nugget</span><span class="p">,</span>
             <span class="n">nugget_est</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
             <span class="n">range_par</span><span class="o">=</span><span class="n">range_par</span><span class="p">,</span>
-            <span class="n">method</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="p">,</span> 
+            <span class="n">method</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">method</span><span class="p">,</span>
             <span class="n">prior_choice</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">prior_choice</span><span class="p">,</span>
             <span class="n">a</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">,</span>
             <span class="n">b</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_b</span><span class="p">,</span>
@@ -666,32 +812,41 @@
             <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
             <span class="n">lower_bound</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">lower_bound</span><span class="p">,</span>
             <span class="n">max_eval</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">max_eval</span><span class="p">,</span>
-            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">)</span> 
-        
+            <span class="n">num_initial_values</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">num_initial_values</span><span class="p">,</span>
+        <span class="p">)</span>
+
         <span class="c1"># predictions and samples of y1 at testing_input using rgasp_emulator</span>
         <span class="n">r_predictions_y1</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">predict_rgasp</span><span class="p">(</span>
-            <span class="n">rgasp_emulator</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span> 
+            <span class="n">rgasp_emulator</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span>
+        <span class="p">)</span>
         <span class="n">predictions_y1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_predictions_y1</span><span class="p">))</span>
-        <span class="n">predictions_mean_y1</span> <span class="o">=</span>  <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">predictions_y1</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">ntest</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
-        
+        <span class="n">predictions_mean_y1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">predictions_y1</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">ntest</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+
         <span class="n">r_samples_y1</span> <span class="o">=</span> <span class="n">RobustGaSP</span><span class="o">.</span><span class="n">Sample</span><span class="p">(</span>
-            <span class="n">rgasp_emulator</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span> <span class="n">num_sample</span><span class="o">=</span><span class="n">nsamples</span><span class="p">,</span>
-            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span>
+            <span class="n">rgasp_emulator</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span>
+            <span class="n">num_sample</span><span class="o">=</span><span class="n">nsamples</span><span class="p">,</span>
+            <span class="n">testing_trend</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">,</span>
+        <span class="p">)</span>
         <span class="n">samples_y1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">r_samples_y1</span><span class="p">)</span>
 
         <span class="c1"># use predictions_mean and samples of y1 to calculate LW term</span>
         <span class="n">LW_term</span> <span class="o">=</span> <span class="p">(</span><span class="n">samples_y1</span> <span class="o">-</span> <span class="n">predictions_mean_y1</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma2_hat</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-        
+
         <span class="c1"># predictions of y1,...,yk using ppgasp_emulator</span>
         <span class="n">predictions</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">testing_input</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">testing_trend</span><span class="p">)</span>
         <span class="n">predictions_mean</span> <span class="o">=</span> <span class="n">predictions</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span>
-        
+
         <span class="n">samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">ntest</span><span class="p">,</span> <span class="n">nresponse</span><span class="p">,</span> <span class="n">nsamples</span><span class="p">))</span>
         <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">nresponse</span><span class="p">):</span>
-            <span class="n">samples</span><span class="p">[:,</span><span class="n">i</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">predictions_mean</span><span class="p">[:,</span> <span class="n">i</span><span class="p">],</span> <span class="p">(</span><span class="n">ntest</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="o">+</span> \
-                             <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma2_hat</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">*</span> <span class="n">LW_term</span>
-            
-        <span class="k">return</span> <span class="n">samples</span></div></div>
+            <span class="n">samples</span><span class="p">[:,</span> <span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">predictions_mean</span><span class="p">[:,</span> <span class="n">i</span><span class="p">],</span> <span class="p">(</span><span class="n">ntest</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+                <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma2_hat</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">*</span> <span class="n">LW_term</span>
+            <span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">samples</span></div>
+</div>
+
 </pre></div>
 
            </div>
@@ -701,7 +856,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2023, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/_modules/psimpy/simulator/mass_point_model.html b/docs/source/_build/html/_modules/psimpy/simulator/mass_point_model.html
index 350ada4a598a9a4e9bbada44bf62950962eda55c..70df450afaa4dafdf0fd657b02c0d495311d86b9 100644
--- a/docs/source/_build/html/_modules/psimpy/simulator/mass_point_model.html
+++ b/docs/source/_build/html/_modules/psimpy/simulator/mass_point_model.html
@@ -15,12 +15,11 @@
     <script src="../../../_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="../../../" id="documentation_options" src="../../../_static/documentation_options.js"></script>
-        <script src="../../../_static/jquery.js"></script>
-        <script src="../../../_static/underscore.js"></script>
-        <script src="../../../_static/_sphinx_javascript_frameworks_compat.js"></script>
-        <script src="../../../_static/doctools.js"></script>
-        <script src="../../../_static/sphinx_highlight.js"></script>
+        <script src="../../../_static/jquery.js?v=5d32c60e"></script>
+        <script src="../../../_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="../../../_static/documentation_options.js?v=938c9ccc"></script>
+        <script src="../../../_static/doctools.js?v=888ff710"></script>
+        <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/js/theme.js"></script>
     <link rel="index" title="Index" href="../../../genindex.html" />
     <link rel="search" title="Search" href="../../../search.html" /> 
@@ -31,14 +30,18 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="../../../index.html" class="icon icon-home"> psimpy
+
+          
+          
+          <a href="../../../index.html" class="icon icon-home">
+            psimpy
           </a>
               <div class="version">
-                0.1.2
+                0.2.0
               </div>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="../../../search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -66,7 +69,7 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="../../../index.html" class="icon icon-home"></a></li>
+      <li><a href="../../../index.html" class="icon icon-home" aria-label="Home"></a></li>
           <li class="breadcrumb-item"><a href="../../index.html">Module code</a></li>
       <li class="breadcrumb-item active">psimpy.simulator.mass_point_model</li>
       <li class="wy-breadcrumbs-aside">
@@ -83,17 +86,19 @@
 <span class="kn">import</span> <span class="nn">linecache</span>
 <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">ode</span>
-<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp2d</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">RegularGridInterpolator</span>
 <span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
 <span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
 
-<div class="viewcode-block" id="MassPointModel"><a class="viewcode-back" href="../../../simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel">[docs]</a><span class="k">class</span> <span class="nc">MassPointModel</span><span class="p">:</span>
+<div class="viewcode-block" id="MassPointModel">
+<a class="viewcode-back" href="../../../simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel">[docs]</a>
+<span class="k">class</span> <span class="nc">MassPointModel</span><span class="p">:</span>
 
-    <span class="sd">&quot;&quot;&quot;Simulate the movement of a masspoint on a topography.&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;Simulate the movement of a masspoint on a topography.&quot;&quot;&quot;</span>
     
     <span class="nd">@staticmethod</span>
     <span class="k">def</span> <span class="nf">_preprocess</span><span class="p">(</span><span class="n">elevation</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">y0</span><span class="p">):</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Preprocess input data.</span>
 
 <span class="sd">        Parameters</span>
@@ -154,11 +159,11 @@
         <span class="n">dzdyy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">dzdy</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
         <span class="n">dzdxy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">dzdx</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
         
-        <span class="n">fgrad_x</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdx</span><span class="p">)</span>
-        <span class="n">fgrad_y</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdy</span><span class="p">)</span>
-        <span class="n">fgrad_xx</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdxx</span><span class="p">)</span>
-        <span class="n">fgrad_yy</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdyy</span><span class="p">)</span>
-        <span class="n">fgrad_xy</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">,</span> <span class="n">dzdxy</span><span class="p">)</span>
+        <span class="n">fgrad_x</span> <span class="o">=</span> <span class="n">RegularGridInterpolator</span><span class="p">((</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">),</span> <span class="n">dzdx</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
+        <span class="n">fgrad_y</span> <span class="o">=</span> <span class="n">RegularGridInterpolator</span><span class="p">((</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">),</span> <span class="n">dzdy</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
+        <span class="n">fgrad_xx</span> <span class="o">=</span> <span class="n">RegularGridInterpolator</span><span class="p">((</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">),</span> <span class="n">dzdxx</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
+        <span class="n">fgrad_yy</span> <span class="o">=</span> <span class="n">RegularGridInterpolator</span><span class="p">((</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">),</span> <span class="n">dzdyy</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
+        <span class="n">fgrad_xy</span> <span class="o">=</span> <span class="n">RegularGridInterpolator</span><span class="p">((</span><span class="n">x_values</span><span class="p">,</span> <span class="n">y_values</span><span class="p">),</span> <span class="n">dzdxy</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
 
         <span class="k">return</span> <span class="n">fgrad_x</span><span class="p">,</span> <span class="n">fgrad_y</span><span class="p">,</span> <span class="n">fgrad_xx</span><span class="p">,</span> <span class="n">fgrad_yy</span><span class="p">,</span> <span class="n">fgrad_xy</span>
 
@@ -167,7 +172,7 @@
     <span class="k">def</span> <span class="nf">_mass_point_model</span><span class="p">(</span>
         <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">coulomb_friction</span><span class="p">,</span> <span class="n">turbulent_friction</span><span class="p">,</span> <span class="n">fgrad_x</span><span class="p">,</span> <span class="n">fgrad_y</span><span class="p">,</span>
         <span class="n">fgrad_xx</span><span class="p">,</span> <span class="n">fgrad_yy</span><span class="p">,</span> <span class="n">fgrad_xy</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">curvature</span><span class="p">):</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Define mass point model (3d) which serves as the callable function</span>
 <span class="sd">        :code:`f(t,alpha,*f_args)` in :class:`scipy.integrate.ode(f)`.</span>
 
@@ -211,8 +216,12 @@
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">ux</span><span class="p">,</span> <span class="n">uy</span> <span class="o">=</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">alpha</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span>
 
-        <span class="n">gradx</span><span class="p">,</span> <span class="n">grady</span><span class="p">,</span> <span class="n">gradxx</span><span class="p">,</span> <span class="n">gradyy</span><span class="p">,</span> <span class="n">gradxy</span> <span class="o">=</span> <span class="n">fgrad_x</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> <span class="n">fgrad_y</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> \
-            <span class="n">fgrad_xx</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> <span class="n">fgrad_yy</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">),</span> <span class="n">fgrad_xy</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span>
+        <span class="n">point</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">])</span>  
+        <span class="n">gradx</span> <span class="o">=</span> <span class="n">fgrad_x</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">grady</span> <span class="o">=</span> <span class="n">fgrad_y</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">gradxx</span> <span class="o">=</span> <span class="n">fgrad_xx</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">gradyy</span> <span class="o">=</span> <span class="n">fgrad_yy</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">gradxy</span> <span class="o">=</span> <span class="n">fgrad_xy</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
 
         <span class="n">sqrt_x</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">gradx</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
         <span class="n">sqrt_y</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">grady</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
@@ -250,7 +259,9 @@
 
         <span class="k">return</span> <span class="n">dalphadt</span>
 
-<div class="viewcode-block" id="MassPointModel.run"><a class="viewcode-back" href="../../../simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel.run">[docs]</a>    <span class="nd">@beartype</span>
+<div class="viewcode-block" id="MassPointModel.run">
+<a class="viewcode-back" href="../../../simulator/mass_point_model.html#psimpy.simulator.mass_point_model.MassPointModel.run">[docs]</a>
+    <span class="nd">@beartype</span>
     <span class="k">def</span> <span class="nf">run</span><span class="p">(</span>
         <span class="bp">self</span><span class="p">,</span> <span class="n">elevation</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">coulomb_friction</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
         <span class="n">turbulent_friction</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span> <span class="n">x0</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span>
@@ -259,7 +270,7 @@
         <span class="n">tend</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">300</span><span class="p">,</span> <span class="n">t0</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
         <span class="n">g</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mf">9.8</span><span class="p">,</span> <span class="n">atol</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="n">rtol</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">,</span>
         <span class="n">curvature</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
-        <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Solve the mass point model using :class:`scipy.integrate.ode` solver</span>
 <span class="sd">        given required input data.</span>
 
@@ -334,8 +345,9 @@
 
         <span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t_all</span><span class="p">))</span>
         <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t_all</span><span class="p">)):</span>
-            <span class="n">gradx</span> <span class="o">=</span> <span class="n">fgrad_x</span><span class="p">(</span><span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
-            <span class="n">grady</span> <span class="o">=</span> <span class="n">fgrad_y</span><span class="p">(</span><span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
+            <span class="n">point</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
+            <span class="n">gradx</span> <span class="o">=</span> <span class="n">fgrad_x</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">grady</span> <span class="o">=</span> <span class="n">fgrad_y</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
             <span class="n">ux</span> <span class="o">=</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
             <span class="n">uy</span> <span class="o">=</span> <span class="n">alpha_all</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="mi">3</span><span class="p">]</span>
             <span class="n">u</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">ux</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">uy</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">ux</span><span class="o">*</span><span class="n">uy</span><span class="o">*</span><span class="n">gradx</span><span class="o">*</span><span class="n">grady</span><span class="o">/</span>
@@ -345,7 +357,9 @@
         <span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">u</span><span class="p">,(</span><span class="nb">len</span><span class="p">(</span><span class="n">u</span><span class="p">),</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
         <span class="n">output</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">t_all</span><span class="p">,</span> <span class="n">alpha_all</span><span class="p">,</span> <span class="n">u</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
         
-        <span class="k">return</span> <span class="n">output</span></div></div>
+        <span class="k">return</span> <span class="n">output</span></div>
+</div>
+
 </pre></div>
 
            </div>
@@ -355,7 +369,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2023, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/_modules/psimpy/simulator/ravaflow3G.html b/docs/source/_build/html/_modules/psimpy/simulator/ravaflow3G.html
index 3f80af51dd4903a997ed1acd2d5f267ba2d7500f..bc5a222d79ee68dab30e1dd5a0a526888bf64d32 100644
--- a/docs/source/_build/html/_modules/psimpy/simulator/ravaflow3G.html
+++ b/docs/source/_build/html/_modules/psimpy/simulator/ravaflow3G.html
@@ -84,9 +84,10 @@
 <span></span><span class="kn">import</span> <span class="nn">os</span>
 <span class="kn">import</span> <span class="nn">linecache</span>
 <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp2d</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">RegularGridInterpolator</span>
 <span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span>
 <span class="kn">from</span> <span class="nn">beartype</span> <span class="kn">import</span> <span class="n">beartype</span>
+<span class="kn">import</span> <span class="nn">warnings</span>
 
 
 <div class="viewcode-block" id="Ravaflow3GMixture">
@@ -178,6 +179,12 @@
 <span class="sd">            `&#39;0&#39;`: Suppress change of direction induced by frictional or viscous forces (default).</span>
 <span class="sd">            `&#39;1&#39;`: Do not suppress the change of direction.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+            <span class="s2">&quot;r.avaflow 3 and lower versions are not supported by its </span><span class="se">\</span>
+<span class="s2">                developers, and their use is discouraged. Therefore, ravaflow3G </span><span class="se">\</span>
+<span class="s2">                module will be deprecated in the future versions.&quot;</span><span class="p">,</span>
+            <span class="ne">FutureWarning</span><span class="p">,</span>
+        <span class="p">)</span>
 
         <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">isdir</span><span class="p">(</span><span class="n">dir_sim</span><span class="p">):</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">dir_sim</span><span class="si">}</span><span class="s2"> does not exist or is not a directory&quot;</span><span class="p">)</span>
@@ -290,6 +297,12 @@
 <span class="sd">            Name of the shell file (including path), which will be called by</span>
 <span class="sd">            `GRASS &lt;https://grass.osgeo.org/&gt;`_ to run the simulation.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+            <span class="s2">&quot;r.avaflow 3 and lower versions are not supported by its </span><span class="se">\</span>
+<span class="s2">                developers, and their use is discouraged. Therefore, ravaflow3G </span><span class="se">\</span>
+<span class="s2">                module will be deprecated in the future versions.&quot;</span><span class="p">,</span>
+            <span class="ne">FutureWarning</span><span class="p">,</span>
+        <span class="p">)</span>
 
         <span class="n">sh_file</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s2">_shell.sh&quot;</span><span class="p">)</span>
         <span class="n">grass_location</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dir_sim</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">prefix</span><span class="si">}</span><span class="s2">_glocation&quot;</span><span class="p">)</span>
@@ -365,6 +378,12 @@
 <span class="sd">        sh_file : str</span>
 <span class="sd">            Name of the shell file (including path).</span>
 <span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+            <span class="s2">&quot;r.avaflow 3 and lower versions are not supported by its </span><span class="se">\</span>
+<span class="s2">                developers, and their use is discouraged. Therefore, ravaflow3G </span><span class="se">\</span>
+<span class="s2">                module will be deprecated in the future versions.&quot;</span><span class="p">,</span>
+            <span class="ne">FutureWarning</span><span class="p">,</span>
+        <span class="p">)</span>
         <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">grass_location</span><span class="p">):</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">grass_location</span><span class="si">}</span><span class="s2"> does not exist&quot;</span><span class="p">)</span>
         <span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">grass_location</span><span class="p">,</span> <span class="s2">&quot;PERMANENT&quot;</span><span class="p">)):</span>
@@ -407,6 +426,12 @@
 <span class="sd">        impact_area : float</span>
 <span class="sd">            A scalar value representing the overall impact area.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+            <span class="s2">&quot;r.avaflow 3 and lower versions are not supported by its </span><span class="se">\</span>
+<span class="s2">                developers, and their use is discouraged. Therefore, ravaflow3G </span><span class="se">\</span>
+<span class="s2">                module will be deprecated in the future versions.&quot;</span><span class="p">,</span>
+            <span class="ne">FutureWarning</span><span class="p">,</span>
+        <span class="p">)</span>
 
         <span class="k">if</span> <span class="n">qoi</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;h&quot;</span><span class="p">,</span> <span class="s2">&quot;v&quot;</span><span class="p">,</span> <span class="s2">&quot;p&quot;</span><span class="p">,</span> <span class="s2">&quot;t&quot;</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;qoi must be &#39;h&#39;, &#39;v&#39;, &#39;p&#39;, or &#39;t&#39;&quot;</span><span class="p">)</span>
@@ -457,6 +482,12 @@
 <span class="sd">        qoi_max : float or numpy array</span>
 <span class="sd">            Maximum value(s) of ``qoi`` in one simulation.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+            <span class="s2">&quot;r.avaflow 3 and lower versions are not supported by its </span><span class="se">\</span>
+<span class="s2">                developers, and their use is discouraged. Therefore, ravaflow3G </span><span class="se">\</span>
+<span class="s2">                module will be deprecated in the future versions.&quot;</span><span class="p">,</span>
+            <span class="ne">FutureWarning</span><span class="p">,</span>
+        <span class="p">)</span>
 
         <span class="k">if</span> <span class="n">qoi</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;h&quot;</span><span class="p">,</span> <span class="s2">&quot;v&quot;</span><span class="p">,</span> <span class="s2">&quot;p&quot;</span><span class="p">,</span> <span class="s2">&quot;t&quot;</span><span class="p">]:</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;qoi must be &#39;h&#39;, &#39;v&#39;, &#39;p&#39;, or &#39;t&#39;&quot;</span><span class="p">)</span>
@@ -504,6 +535,12 @@
 <span class="sd">            Consist of maximum value(s) of ``qoi`` at each location.</span>
 <span class="sd">            Shape of :code:`(nloc,)`.</span>
 <span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+            <span class="s2">&quot;r.avaflow 3 and lower versions are not supported by its </span><span class="se">\</span>
+<span class="s2">                developers, and their use is discouraged. Therefore, ravaflow3G </span><span class="se">\</span>
+<span class="s2">                module will be deprecated in the future versions.&quot;</span><span class="p">,</span>
+            <span class="ne">FutureWarning</span><span class="p">,</span>
+        <span class="p">)</span>
 
         <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">loc</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">loc</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mi">2</span><span class="p">):</span>
             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
@@ -546,9 +583,12 @@
         <span class="n">qoi_max_raster</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="n">qoi_max_raster_asc</span><span class="p">,</span> <span class="n">skiprows</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>
         <span class="n">qoi_max_raster</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">rot90</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">qoi_max_raster</span><span class="p">))</span>
 
-        <span class="n">f_qoi_max</span> <span class="o">=</span> <span class="n">interp2d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">qoi_max_raster</span><span class="p">)</span>
+        <span class="n">f_qoi_max</span> <span class="o">=</span> <span class="n">RegularGridInterpolator</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">),</span> <span class="n">qoi_max_raster</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
 
-        <span class="n">qoi_max_loc</span> <span class="o">=</span> <span class="p">[</span><span class="nb">float</span><span class="p">(</span><span class="n">f_qoi_max</span><span class="p">(</span><span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">loc</span><span class="p">))]</span>
+        <span class="n">qoi_max_loc</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">loc</span><span class="p">)):</span>
+            <span class="n">point</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">loc</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
+            <span class="n">qoi_max_loc</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">f_qoi_max</span><span class="p">(</span><span class="n">point</span><span class="p">)[</span><span class="mi">0</span><span class="p">]))</span>
 
         <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">qoi_max_loc</span><span class="p">)</span></div>
 </div>
@@ -562,7 +602,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/api.html b/docs/source/_build/html/api.html
index 3a2aa22767001ece5c2ab3b234343f71c4209c26..ba923a748889f7c1812e1f59b74f7890fe2ac291 100644
--- a/docs/source/_build/html/api.html
+++ b/docs/source/_build/html/api.html
@@ -114,7 +114,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/emulator/index.html b/docs/source/_build/html/auto_examples/emulator/index.html
index fbfd6137107419329ab8b09573d0f9a5b9d19eaa..e432f784b64fe1d3ab094659640ba412b2dba077 100644
--- a/docs/source/_build/html/auto_examples/emulator/index.html
+++ b/docs/source/_build/html/auto_examples/emulator/index.html
@@ -127,7 +127,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/emulator/plot_ppgasp.html b/docs/source/_build/html/auto_examples/emulator/plot_ppgasp.html
index 50690eb7582b16182d6ae84da96f98bafb665222..01f003311ac1f49b0e1fe02a533c68e15ae0b796 100644
--- a/docs/source/_build/html/auto_examples/emulator/plot_ppgasp.html
+++ b/docs/source/_build/html/auto_examples/emulator/plot_ppgasp.html
@@ -239,7 +239,7 @@ Here, we make predictions at testing input points <code class="docutils literal
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/emulator/plot_scalargasp.html b/docs/source/_build/html/auto_examples/emulator/plot_scalargasp.html
index bde84bccefd553df638464b2c53b3134aaf91cd0..94aca8415a3edcdf42523ec8224077c7ca975cda 100644
--- a/docs/source/_build/html/auto_examples/emulator/plot_scalargasp.html
+++ b/docs/source/_build/html/auto_examples/emulator/plot_scalargasp.html
@@ -247,7 +247,7 @@ is estimated from the noisy training data.</p></li>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/emulator/sg_execution_times.html b/docs/source/_build/html/auto_examples/emulator/sg_execution_times.html
index 048c435e7bc78ab9402acd2d18755dd2def93bb0..274832523ffb878780fa1f348ec7202e89ce1415 100644
--- a/docs/source/_build/html/auto_examples/emulator/sg_execution_times.html
+++ b/docs/source/_build/html/auto_examples/emulator/sg_execution_times.html
@@ -106,7 +106,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/inference/index.html b/docs/source/_build/html/auto_examples/inference/index.html
index 85cc9e7881504effc3ab86376fde869e0839c490..ffa84a9e27135f03bec69126add1bedd69c20829 100644
--- a/docs/source/_build/html/auto_examples/inference/index.html
+++ b/docs/source/_build/html/auto_examples/inference/index.html
@@ -127,7 +127,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/inference/plot_active_learning.html b/docs/source/_build/html/auto_examples/inference/plot_active_learning.html
index 9f2e0749a5e15508ddecd5c3186aa8765a3440c3..6a7fa58022563dee65123402ee33575e530ab467 100644
--- a/docs/source/_build/html/auto_examples/inference/plot_active_learning.html
+++ b/docs/source/_build/html/auto_examples/inference/plot_active_learning.html
@@ -1154,7 +1154,7 @@ the estimated posterior.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/inference/plot_bayes_inference.html b/docs/source/_build/html/auto_examples/inference/plot_bayes_inference.html
index 3b3d9e8b990c740a99020ed8a489d6f4c4885df7..5f3eaac52a29c418499e4d3f861c596e157f49f6 100644
--- a/docs/source/_build/html/auto_examples/inference/plot_bayes_inference.html
+++ b/docs/source/_build/html/auto_examples/inference/plot_bayes_inference.html
@@ -224,7 +224,7 @@ the <a class="reference internal" href="../../inference/bayes_inference.html#psi
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/inference/sg_execution_times.html b/docs/source/_build/html/auto_examples/inference/sg_execution_times.html
index a81359fb9f19315b38f14181b7010a8b4b9f8c93..94fe048112bd49c950d15d2d9681313f61925437 100644
--- a/docs/source/_build/html/auto_examples/inference/sg_execution_times.html
+++ b/docs/source/_build/html/auto_examples/inference/sg_execution_times.html
@@ -106,7 +106,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sampler/index.html b/docs/source/_build/html/auto_examples/sampler/index.html
index 9779dc3e4b865c1456ab8f2db388de093062822e..e2fca6680032e77babce0786d01ae8628927ae18 100644
--- a/docs/source/_build/html/auto_examples/sampler/index.html
+++ b/docs/source/_build/html/auto_examples/sampler/index.html
@@ -131,7 +131,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sampler/plot_latin.html b/docs/source/_build/html/auto_examples/sampler/plot_latin.html
index 9d049087a9be871da15127612fb37fdcf87b40d6..db24cc7fdfd1e007d09d285acf057c4a9fe81c54 100644
--- a/docs/source/_build/html/auto_examples/sampler/plot_latin.html
+++ b/docs/source/_build/html/auto_examples/sampler/plot_latin.html
@@ -197,7 +197,7 @@ we can use the <cite>center</cite> criterion to draw <span class="math notransla
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sampler/plot_metropolis_hastings.html b/docs/source/_build/html/auto_examples/sampler/plot_metropolis_hastings.html
index ead3506534f54f3e7d90ad3ae0209786511c9996..e7b308adeab3f617ff4cf4a99314eb807e22c7a4 100644
--- a/docs/source/_build/html/auto_examples/sampler/plot_metropolis_hastings.html
+++ b/docs/source/_build/html/auto_examples/sampler/plot_metropolis_hastings.html
@@ -219,7 +219,7 @@ number of samples.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sampler/plot_saltelli.html b/docs/source/_build/html/auto_examples/sampler/plot_saltelli.html
index e8483263a58bcafda6caeff9449a772b3ac89cab..eaf24ea01e278c45e6a8dd3d499a745bbbd482a4 100644
--- a/docs/source/_build/html/auto_examples/sampler/plot_saltelli.html
+++ b/docs/source/_build/html/auto_examples/sampler/plot_saltelli.html
@@ -197,7 +197,7 @@ Sobol’ index in that case.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sampler/sg_execution_times.html b/docs/source/_build/html/auto_examples/sampler/sg_execution_times.html
index 48b7902aff4b8ad54d277546ffc8ab3a186c2cac..d442642c470490b84838db03a451150313ca5e19 100644
--- a/docs/source/_build/html/auto_examples/sampler/sg_execution_times.html
+++ b/docs/source/_build/html/auto_examples/sampler/sg_execution_times.html
@@ -110,7 +110,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sensitivity/index.html b/docs/source/_build/html/auto_examples/sensitivity/index.html
index 44a7cb02d116028015073bfeceda82c7b928c9e3..43dee7ff6ab1a9a8055c36eb32436a059b3e6b00 100644
--- a/docs/source/_build/html/auto_examples/sensitivity/index.html
+++ b/docs/source/_build/html/auto_examples/sensitivity/index.html
@@ -123,7 +123,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sensitivity/plot_sobol_analyze.html b/docs/source/_build/html/auto_examples/sensitivity/plot_sobol_analyze.html
index 087357194050024dc08b3eba3b5276967d1a489a..3da2b588bed8bdaf38135e4a3f2aef2d67d45e03 100644
--- a/docs/source/_build/html/auto_examples/sensitivity/plot_sobol_analyze.html
+++ b/docs/source/_build/html/auto_examples/sensitivity/plot_sobol_analyze.html
@@ -343,7 +343,7 @@ look like.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/sensitivity/sg_execution_times.html b/docs/source/_build/html/auto_examples/sensitivity/sg_execution_times.html
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--- a/docs/source/_build/html/auto_examples/sensitivity/sg_execution_times.html
+++ b/docs/source/_build/html/auto_examples/sensitivity/sg_execution_times.html
@@ -102,7 +102,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/simulator/index.html b/docs/source/_build/html/auto_examples/simulator/index.html
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--- a/docs/source/_build/html/auto_examples/simulator/index.html
+++ b/docs/source/_build/html/auto_examples/simulator/index.html
@@ -135,7 +135,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/auto_examples/simulator/plot_mass_point_model.html b/docs/source/_build/html/auto_examples/simulator/plot_mass_point_model.html
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--- a/docs/source/_build/html/auto_examples/simulator/plot_mass_point_model.html
+++ b/docs/source/_build/html/auto_examples/simulator/plot_mass_point_model.html
@@ -241,7 +241,7 @@ Following plots show the simulation results.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/auto_examples/simulator/plot_ravaflow24.html b/docs/source/_build/html/auto_examples/simulator/plot_ravaflow24.html
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--- a/docs/source/_build/html/auto_examples/simulator/plot_ravaflow24.html
+++ b/docs/source/_build/html/auto_examples/simulator/plot_ravaflow24.html
@@ -265,7 +265,7 @@ maximum flow velocity at specific locations:</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/simulator/plot_ravaflow3G.html b/docs/source/_build/html/auto_examples/simulator/plot_ravaflow3G.html
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--- a/docs/source/_build/html/auto_examples/simulator/plot_ravaflow3G.html
+++ b/docs/source/_build/html/auto_examples/simulator/plot_ravaflow3G.html
@@ -260,7 +260,7 @@ Maximum flow velocity at location [1500 2000] is 34.779 m/s^2
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/simulator/plot_run_mass_point_model.html b/docs/source/_build/html/auto_examples/simulator/plot_run_mass_point_model.html
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--- a/docs/source/_build/html/auto_examples/simulator/plot_run_mass_point_model.html
+++ b/docs/source/_build/html/auto_examples/simulator/plot_run_mass_point_model.html
@@ -284,7 +284,7 @@ numpy array.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/auto_examples/simulator/plot_run_ravaflow24.html b/docs/source/_build/html/auto_examples/simulator/plot_run_ravaflow24.html
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--- a/docs/source/_build/html/auto_examples/simulator/plot_run_ravaflow24.html
+++ b/docs/source/_build/html/auto_examples/simulator/plot_run_ravaflow24.html
@@ -301,7 +301,7 @@ numpy array.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/auto_examples/simulator/plot_run_ravaflow3G.html b/docs/source/_build/html/auto_examples/simulator/plot_run_ravaflow3G.html
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@@ -313,7 +313,7 @@ numpy array.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/auto_examples/simulator/sg_execution_times.html b/docs/source/_build/html/auto_examples/simulator/sg_execution_times.html
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+++ b/docs/source/_build/html/auto_examples/simulator/sg_execution_times.html
@@ -114,7 +114,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/changelog.html b/docs/source/_build/html/changelog.html
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--- a/docs/source/_build/html/changelog.html
+++ b/docs/source/_build/html/changelog.html
@@ -85,6 +85,15 @@
              
   <section id="changes">
 <h1>Changes<a class="headerlink" href="#changes" title="Link to this heading"></a></h1>
+<section id="v1-0-0">
+<h2>v1.0.0<a class="headerlink" href="#v1-0-0" title="Link to this heading"></a></h2>
+<ul class="simple">
+<li><p>Removed the <cite>simulator/ravaflow24</cite> module.</p></li>
+<li><p>Replaced deprecated <cite>scipy.interpolate.interp2d</cite> with <cite>scipy.interpolate.RegularGridInterpolator</cite> to maintain compatibility with newer versions of SciPy.</p></li>
+<li><p>Added citation information to the README.</p></li>
+<li><p>Added repeated k-fold validation for <cite>emulator/robustgasp</cite> module.</p></li>
+</ul>
+</section>
 <section id="v0-2-1">
 <h2>v0.2.1<a class="headerlink" href="#v0-2-1" title="Link to this heading"></a></h2>
 <ul class="simple">
@@ -135,7 +144,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/emulator/index.html b/docs/source/_build/html/emulator/index.html
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--- a/docs/source/_build/html/emulator/index.html
+++ b/docs/source/_build/html/emulator/index.html
@@ -125,7 +125,7 @@ multiple values as output.</p></li>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/emulator/robustgasp.html b/docs/source/_build/html/emulator/robustgasp.html
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--- a/docs/source/_build/html/emulator/robustgasp.html
+++ b/docs/source/_build/html/emulator/robustgasp.html
@@ -323,7 +323,7 @@ Default is <span class="math notranslate nohighlight">\(2\)</span>.</p></li>
 </dl>
 <dl class="py method">
 <dt class="sig sig-object py" id="psimpy.emulator.robustgasp.ScalarGaSP.train">
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+<span class="sig-name descname"><span class="pre">train</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">design</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">response</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">verbose</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/psimpy/emulator/robustgasp.html#ScalarGaSP.train"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#psimpy.emulator.robustgasp.ScalarGaSP.train" title="Link to this definition"></a></dt>
 <dd><p>Train a scalar GP given training data.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -338,6 +338,8 @@ dimension. If <span class="math notranslate nohighlight">\(ndim=1\)</span>, both
 If <cite>None</cite>, a <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> matrix of ones is used.
 If <span class="math notranslate nohighlight">\(q=1\)</span>, both <code class="code docutils literal notranslate"><span class="pre">(ntrain,</span> <span class="pre">1)</span></code> and <code class="code docutils literal notranslate"><span class="pre">(ntrain,)</span></code>
 <code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> are valid.</p></li>
+<li><p><strong>verbose</strong> (<em>bool</em><em>, </em><em>optional</em>) – If <cite>‘True’</cite>, Displays detailed information.
+Default is <cite>True</cite>.</p></li>
 </ul>
 </dd>
 <dt class="field-even">Return type<span class="colon">:</span></dt>
@@ -599,7 +601,7 @@ emulator at <code class="docutils literal notranslate"><span class="pre">testing
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/examples.html b/docs/source/_build/html/examples.html
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+++ b/docs/source/_build/html/examples.html
@@ -114,7 +114,7 @@
   <hr/>
 
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-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/genindex.html b/docs/source/_build/html/genindex.html
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+++ b/docs/source/_build/html/genindex.html
@@ -278,7 +278,7 @@
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-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/index.html b/docs/source/_build/html/index.html
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--- a/docs/source/_build/html/index.html
+++ b/docs/source/_build/html/index.html
@@ -90,7 +90,7 @@
 <dd class="field-odd"><p>0.2.1</p>
 </dd>
 <dt class="field-even">Date<span class="colon">:</span></dt>
-<dd class="field-even"><p>Mar 18, 2024</p>
+<dd class="field-even"><p>Mar 22, 2025</p>
 </dd>
 </dl>
 <section id="contents">
@@ -137,7 +137,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/inference/active_learning.html b/docs/source/_build/html/inference/active_learning.html
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--- a/docs/source/_build/html/inference/active_learning.html
+++ b/docs/source/_build/html/inference/active_learning.html
@@ -284,7 +284,7 @@ than <span class="math notranslate nohighlight">\(ninit+niter\)</span>.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/inference/bayes_inference.html b/docs/source/_build/html/inference/bayes_inference.html
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--- a/docs/source/_build/html/inference/bayes_inference.html
+++ b/docs/source/_build/html/inference/bayes_inference.html
@@ -299,7 +299,7 @@ acceptance ratio.</p></li>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/source/_build/html/inference/index.html b/docs/source/_build/html/inference/index.html
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+++ b/docs/source/_build/html/inference/index.html
@@ -119,7 +119,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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diff --git a/docs/source/_build/html/quickstart.html b/docs/source/_build/html/quickstart.html
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--- a/docs/source/_build/html/quickstart.html
+++ b/docs/source/_build/html/quickstart.html
@@ -171,7 +171,7 @@ before starting PSimPy to use a custom R environment.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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@@ -159,7 +159,7 @@
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   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/sampler/index.html b/docs/source/_build/html/sampler/index.html
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--- a/docs/source/_build/html/sampler/index.html
+++ b/docs/source/_build/html/sampler/index.html
@@ -120,7 +120,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/sampler/latin.html b/docs/source/_build/html/sampler/latin.html
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+++ b/docs/source/_build/html/sampler/latin.html
@@ -187,7 +187,7 @@ samples accordingly.</p>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
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--- a/docs/source/_build/html/sampler/metropolis_hastings.html
+++ b/docs/source/_build/html/sampler/metropolis_hastings.html
@@ -216,7 +216,7 @@ acceptance ratio.</p></li>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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+++ b/docs/source/_build/html/sampler/saltelli.html
@@ -170,7 +170,7 @@ is <cite>True</cite>. Shape of <code class="code docutils literal notranslate"><
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
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+++ b/docs/source/_build/html/search.html
@@ -102,7 +102,7 @@
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-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
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@@ -1 +1 @@
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--- a/docs/source/_build/html/sensitivity/index.html
+++ b/docs/source/_build/html/sensitivity/index.html
@@ -116,7 +116,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/sensitivity/sobol.html b/docs/source/_build/html/sensitivity/sobol.html
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--- a/docs/source/_build/html/sensitivity/sobol.html
+++ b/docs/source/_build/html/sensitivity/sobol.html
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   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
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--- a/docs/source/_build/html/simulator/index.html
+++ b/docs/source/_build/html/simulator/index.html
@@ -138,7 +138,7 @@ installed by the user.</p>
   <hr/>
 
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+    <p>&#169; Copyright 2025, Hu Zhao.</p>
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   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
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diff --git a/docs/source/_build/html/simulator/ravaflow3G.html b/docs/source/_build/html/simulator/ravaflow3G.html
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   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
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index 7f2716da52ae478f28e51c6ed5e7191a813a9c8d..0d71402e5888fbf59e21b523224e0a0a01a500ad 100644
--- a/docs/source/_build/html/simulator/run_simulator.html
+++ b/docs/source/_build/html/simulator/run_simulator.html
@@ -227,7 +227,7 @@ Default is the number of CPUs on the host.</p></li>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2024, Hu Zhao.</p>
+    <p>&#169; Copyright 2025, Hu Zhao.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/pyproject.toml b/pyproject.toml
index 5387b190dce10531c2005104a6df1a6dd6a6eb32..8c3bd395f5b5c7cccc8bbb461f936ac3d6d0b5e8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "psimpy"
-version = "0.2.1"
+version = "1.0.0"
 description = "Predictive and probabilistic simulation tools."
 authors = ["Hu Zhao"]
 license = "MIT"
diff --git a/src/psimpy/simulator/__init__.py b/src/psimpy/simulator/__init__.py
index 78b86034ef6baba0aa10c877f89de4f7e2a44904..5ffea9be2d42dfd88ec9841635c4b229b4734f03 100644
--- a/src/psimpy/simulator/__init__.py
+++ b/src/psimpy/simulator/__init__.py
@@ -1,4 +1,3 @@
 from psimpy.simulator.mass_point_model import MassPointModel
-from psimpy.simulator.ravaflow24 import Ravaflow24Mixture
 from psimpy.simulator.ravaflow3G import Ravaflow3GMixture
 from psimpy.simulator.run_simulator import RunSimulator
diff --git a/src/psimpy/simulator/ravaflow24.py b/src/psimpy/simulator/ravaflow24.py
deleted file mode 100755
index d8f22d96eeca7309931db894d15b9e3bbc668de2..0000000000000000000000000000000000000000
--- a/src/psimpy/simulator/ravaflow24.py
+++ /dev/null
@@ -1,474 +0,0 @@
-import os
-import linecache
-import numpy as np
-from scipy.interpolate import interp2d
-from typing import Union
-from beartype import beartype
-import warnings
-
-
-class Ravaflow24Mixture:
-    @beartype
-    def __init__(
-        self,
-        dir_sim: str,
-        time_step: Union[float, int] = 10,
-        time_end: Union[float, int] = 300,
-        cfl: float = 0.4,
-        time_step_length: float = 0.001,
-        conversion_control: str = "0",
-        curvature_control: str = "1",
-        surface_control: str = "0",
-        entrainment_control: str = "0",
-        shear_velocity_coef: float = 0.05,
-        basal_friction_diff: float = 0.0,
-        stopping_control: str = "0",
-        stopping_threshold: float = 0.0,
-        friction_control: str = "0",
-    ) -> None:
-        """
-        `r.avaflow 2.4 Mixture model` (Voellmy-type shallow flow model).
-
-        Parameters
-        ----------
-        dir_sim : str
-            Directory to save output files generated by `r.avaflow`.
-        time_step : float or int
-            Time step for simulation, in seconds.
-        time_end : float or int
-            End time for simulation, in seconds.
-        cfl : float
-            CFL criterion, a value being equal or smaller than 0.5.
-        time_step_length : float
-            If ``cfl`` is not applicable, ``time_step_length`` is used.
-            In seconds. Recommended range is around :math:`0.1` to :math:`0.5`.
-        conversion_control : str
-            `'0'`: no conversion of flow heights to flow depths.
-            `'1'`: conversion is applied.
-        curvature_control : str
-            `'0'`: curvature is neglected.
-            `'1'`: curvature is considered in the decelerating source terms.
-            `'2'`: curvature is considered in all relevant terms.
-        surface_control : str
-            `'0'`: no balancing of forces.
-            `'1'`: apply balancing of forces.
-        entrainment_control : str
-            `'0'`: no entrainment.
-            `'1'`: the entrainment coefficient is multiplied with flow momentum.
-            `'2'`: simplified entrainment and deposition model is used.
-            `'3'`: combination of `'1'` for entrainmnet and `'2'` for deposition.
-            `'4'`: acceleration-deceleration entrainment and deposition model.
-        shear_velocity_coef : float
-            Only used with ``entrainment_control`` being `'2'` or `'3'`, range
-            :math:`[0,1]`.
-        basal_friction_diff : float
-            Difference between the basal friction angles of the basal surface
-            and the flow, in degrees. Only used with ``entrainment_control``
-            being `'2'` or `'3'`.
-        stopping_control : str
-            `'0'`: no stopping control is used.
-            `'1'`: stop if the flow kinetic energy is equal or smaller than a
-            given threshold.
-            `'2'`: stop if the flow momentum is equal or smaller than a given
-            threshold.
-            `'3'`: stop if the dynamic flow pressure of all raster cells is
-            euqal or smaller than a given threshold.
-        stopping_threshold : float
-            Threshold value for ``stopping_control``.
-            If ``stopping_control`` is `'1'` or `'2'`, ``stopping_threshold``
-            has to be given as the maximum value reached during the flow.
-            If ``stopping_control`` is `'3'`, the pressure threshold has to be
-            specified.
-        friction_control : str, optional
-            `'0'`: no dynamic adaptation of friction parameters.
-            `'1'`: dynamic adaptation of friction parameters (ignored for the
-            mixture model).
-
-        """
-        warnings.warn(
-            "r.avaflow 2.4pre and lower versions are not supported by its \
-                developers, and their use is discouraged. Therefore, ravaflow24 \
-                module will be deprecated in the future versions. Please use \
-                ravaflow3G module instead.",
-            FutureWarning,
-        )
-
-        if not os.path.isdir(dir_sim):
-            raise ValueError(f"{dir_sim} does not exist or is not a directory")
-        self.dir_sim = dir_sim
-
-        self.time_step = time_step
-        self.time_end = time_end
-        self.cfl = cfl
-        self.time_step_length = time_step_length
-
-        if conversion_control not in ["0", "1"]:
-            raise ValueError("convresion_control must be '0' or '1'")
-        self.conversion_control = conversion_control
-
-        if curvature_control not in ["0", "1", "2"]:
-            raise ValueError("curvature_control must be '0' or '1' or '2'")
-        self.curvature_control = curvature_control
-
-        if surface_control not in ["0", "1"]:
-            raise ValueError("surface_control must be '0' or '1'")
-        self.surface_control = surface_control
-
-        if entrainment_control not in ["0", "1", "2", "3", "4"]:
-            raise ValueError("entrainment_control must be '0', '1', '2', '3', or '4'")
-        self.entrainment_control = entrainment_control
-
-        self.shear_velocity_coef = shear_velocity_coef
-        self.basal_friction_diff = basal_friction_diff
-
-        if stopping_control not in ["0", "1", "2", "3"]:
-            raise ValueError("stopping_control must be '0', '1', '2', or '3'")
-        self.stopping_control = stopping_control
-
-        self.stopping_threshold = stopping_threshold
-
-        if friction_control not in ["0", "1"]:
-            raise ValueError("friction_control must be '0' or '1'")
-        self.friction_control = friction_control
-
-    @beartype
-    def preprocess(
-        self,
-        prefix: str,
-        elevation: str,
-        hrelease: str,
-        cellsize: Union[float, int, np.floating, np.integer] = 20,
-        hrelease_ratio: Union[float, np.integer] = 1.0,
-        internal_friction: Union[float, int, np.floating, np.integer] = 35,
-        basal_friction: Union[float, int, np.floating, np.integer] = 20,
-        turbulent_friction: Union[float, int, np.floating, np.integer] = 3,
-        entrainment_coef: Union[float, np.floating] = -7.0,
-        EPSG: Union[str, None] = None,
-    ) -> tuple[str, str]:
-        """
-        Preprocess simulation input data simulation.
-
-        Parameters
-        ----------
-        prefix : str
-            Prefix required by `r.avaflow` to name output files.
-        elevation : str
-            Name of elevation raster file (including its path).
-            The file format should be supported by `GDAL`.
-            Its unit is in meters.
-        hrelease : str
-            Name of release height raster file (including its path).
-            The file format should be supported by `GDAL`.
-            Its unit is in meters.
-        cellsize : float or int, optional
-            Cell size in meters to be used for simulation.
-        hrelease_ratio : float, optional
-            A positive value to multiple ``hrelease`` in order to control
-            the release volume.
-        internal_friction : float or int, optional
-            Internal friction angle, in degrees, range :math:`[0,90)`.
-        basal_friction : float or int, optional
-            Basal friction angle, in degrees, range :math:`[0,90)`.
-        turbulent_friction : float or int, optional
-            Logarithm with base :math:`10` of the turbulent friction, in
-            :math:`m/s^2`.
-        entrainment_coef : float, optional
-            Logarithm with base :math:`10` of the entrainment coefficient,
-            except for :math:`0` meaning no entrainment.
-        EPSG : str, optional
-            `EPSG` (European Petroleum Survey Group) code to create
-            `GRASS Location <https://grass.osgeo.org/grass82/manuals/grass_database.html>`_.
-            If `None`, ``elevation`` must be a georeferenced file which has
-            metadata to create the `GRASS Location`.
-
-        Returns
-        -------
-        grass_location : str
-            Name of the `GRASS Location` (including path).
-        sh_file : str
-            Name of the shell file (including path), which will be called by
-            `GRASS <https://grass.osgeo.org/>`_ to run the simulation.
-        """
-        warnings.warn(
-            "r.avaflow 2.4pre and lower versions are not supported by its \
-                developers, and their use is discouraged. Therefore, ravaflow24 \
-                module will be deprecated in the future versions. Please use \
-                ravaflow3G module instead.",
-            FutureWarning,
-        )
-
-        sh_file = os.path.join(self.dir_sim, f"{prefix}_shell.sh")
-        grass_location = os.path.join(self.dir_sim, f"{prefix}_glocation")
-        results_dir = os.path.join(self.dir_sim, f"{prefix}_results")
-
-        if (
-            os.path.exists(sh_file)
-            or os.path.exists(grass_location)
-            or os.path.exists(results_dir)
-        ):
-            raise ValueError(
-                f"File(s) with prefix={prefix} already exists in {self.dir_sim}."
-                f" Move or delete conflicting files, or use another prefix."
-            )
-
-        if not os.path.exists(elevation):
-            raise ValueError(f"{elevation} does not exist")
-
-        if not os.path.exists(hrelease):
-            raise ValueError(f"{hrelease} does not exist")
-
-        # create grass location
-        if EPSG is None:
-            os.system(f"grass -e -c {elevation} {grass_location}")
-        else:
-            os.system(f"grass -e -c EPSG:{EPSG} {grass_location}")
-
-        # create shell file
-        with open(sh_file, "w") as sh:
-            sh.write("# import elevation raster \n")
-            sh.write(f"r.in.gdal -o input={elevation} output=elev --overwrite")
-            sh.write("\n\n")
-
-            sh.write("# set region based on elev \n")
-            sh.write("g.region raster=elev \n\n")
-
-            sh.write("# import hrelease raster \n")
-            sh.write(f"r.in.gdal -o input={hrelease} output=raw_hrel --overwrite")
-            sh.write("\n\n")
-
-            sh.write(f'r.mapcalc "hrel = raw_hrel*{hrelease_ratio}" --overwrite')
-            sh.write("\n\n")
-
-            sh.write(
-                f"r.avaflow -e -a prefix={prefix} cellsize={cellsize} phases=x "
-                f"elevation=elev hrelease=hrel "
-                f"friction={internal_friction},{basal_friction},"
-                f"{turbulent_friction} "
-                f"basal={entrainment_coef},{self.shear_velocity_coef},"
-                f"{self.basal_friction_diff},{self.stopping_threshold} "
-                f"controls={self.conversion_control},{self.curvature_control},"
-                f"{self.surface_control},{self.entrainment_control},"
-                f"{self.stopping_control},{self.friction_control} "
-                f"time={self.time_step},{self.time_end} "
-                f"cfl={self.cfl},{self.time_step_length}"
-            )
-
-        return grass_location, sh_file
-
-    @beartype
-    def run(self, grass_location: str, sh_file: str) -> None:
-        """
-        Run simulation.
-
-        Parameters
-        ----------
-        grass_location : str
-            Name of the `GRASS Location` (including path).
-        sh_file : str
-            Name of the shell file (including path).
-        """
-        warnings.warn(
-            "r.avaflow 2.4pre and lower versions are not supported by its \
-                developers, and their use is discouraged. Therefore, ravaflow24 \
-                module will be deprecated in the future versions. Please use \
-                ravaflow3G module instead.",
-            FutureWarning,
-        )
-        if not os.path.exists(grass_location):
-            raise ValueError(f"{grass_location} does not exist")
-        if not os.path.exists(os.path.join(grass_location, "PERMANENT")):
-            raise ValueError(f"{grass_location} is not a grass location")
-
-        if not os.path.exists(sh_file):
-            raise ValueError(f"{sh_file} does not exist")
-
-        grass_mapset = os.path.join(grass_location, "PERMANENT", "")
-
-        os.chdir(self.dir_sim)
-        os.system(f"grass {grass_mapset} --exec sh {sh_file}")
-
-    def extract_impact_area(
-        self, prefix: str, qoi: str = "h", threshold: Union[float, int] = 0.5
-    ) -> float:
-        """
-        Extract impact area defined by a given quantity of interest and its
-        threshold.
-
-        Parameters
-        ----------
-        prefix : str
-            Prefix used by `r.avaflow` to name output files.
-        qoi : str
-            Quantity of interest to determine the impact area.
-            `'h'`: maximum flow height, in meters.
-            `'v'`: maximum flow velocity, in :math:`m/s`.
-            `'p'`: maximum flow pressure, in :math:`Pa`.
-            `'t'`: maximum flow kinetic energy, in :math:`J`.
-        threshold : float or int
-            Threshold of ``qoi`` to determine impact area. Areas where ``qoi``
-            is larger than ``threshold`` are regarded as impar area.
-
-        Returns
-        -------
-        impact_area : float
-            A scalar value representing the overall impact area.
-        """
-        warnings.warn(
-            "r.avaflow 2.4pre and lower versions are not supported by its \
-                developers, and their use is discouraged. Therefore, ravaflow24 \
-                module will be deprecated in the future versions. Please use \
-                ravaflow3G module instead.",
-            FutureWarning,
-        )
-
-        if qoi not in ["h", "v", "p", "t"]:
-            raise ValueError("qoi must be 'h', 'v', 'p', or 't'")
-
-        qoi_max_raster_asc = os.path.join(
-            self.dir_sim,
-            f"{prefix}_results",
-            f"{prefix}_ascii",
-            f"{prefix}_{qoi}flow_max.asc",
-        )
-        qoi_max_raster = np.loadtxt(qoi_max_raster_asc, skiprows=6)
-
-        cellsize = linecache.getline(qoi_max_raster_asc, 5)
-        cellsize = float(cellsize.split()[-1].strip())
-
-        impact_area = (
-            np.sum(np.where(qoi_max_raster > threshold, 1, 0)) * (cellsize) ** 2
-        )
-
-        return float(impact_area)
-
-    def extract_qoi_max(
-        self, prefix: str, qoi: str, aggregate: bool = True
-    ) -> Union[float, np.ndarray]:
-        """
-        Extract the maximum value(s) of a quantity of interest.
-
-        Parameters
-        ----------
-        prefix : str
-            Prefix used by `r.avaflow` to name output files.
-        qoi : str
-            Quantity of interest.
-            `'h'`: maximum flow height, in meters.
-            `'v'`: maximum flow velocity, in :math:`m/s`.
-            `'p'`: maximum flow pressure, in :math:`Pa`.
-            `'t'`: maximum flow kinetic energy, in :math:`J`.
-        aggregate : bool
-            If `True`, returns the overall maximum value over all spatio-tempo
-            grids. If `False`, returns the maximum values over all time steps at
-            each spatio location, namely a raster of maximum values.
-
-        Returns
-        -------
-        qoi_max : float or numpy array
-            Maximum value(s) of ``qoi`` in one simulation.
-        """
-        warnings.warn(
-            "r.avaflow 2.4pre and lower versions are not supported by its \
-                developers, and their use is discouraged. Therefore, ravaflow24 \
-                module will be deprecated in the future versions. Please use \
-                ravaflow3G module instead.",
-            FutureWarning,
-        )
-
-        if qoi not in ["h", "v", "p", "t"]:
-            raise ValueError("qoi must be 'h', 'v', 'p', or 't'")
-
-        qoi_max_raster_asc = os.path.join(
-            self.dir_sim,
-            f"{prefix}_results",
-            f"{prefix}_ascii",
-            f"{prefix}_{qoi}flow_max.asc",
-        )
-        qoi_max_raster = np.loadtxt(qoi_max_raster_asc, skiprows=6)
-
-        if aggregate:
-            return float(np.max(qoi_max_raster))
-        else:
-            return np.rot90(np.transpose(qoi_max_raster))
-
-    def extract_qoi_max_loc(self, prefix: str, loc: np.ndarray, qoi: str) -> np.ndarray:
-        """
-        Extract maximum value(s) of a quantity of interest at specific
-        location(s).
-
-        Parameters
-        ----------
-        prefix : str
-            Prefix used by `r.avaflow` to name output files.
-        loc : numpy array
-            Coordinates of interested locations. Shape :code:`(nloc, 2)`, where
-            ``nloc`` is the number of interested locations.
-            :code:`loc[:,0]` corresponds to `x` coordinates and
-            :code:`loc[:,1]` to `y` coordinates.
-        qoi : str
-            Quantity of interest.
-            `'h'`: maximum flow height, in meters.
-            `'v'`: maximum flow velocity, in :math:`m/s`.
-            `'p'`: maximum flow pressure, in :math:`Pa`.
-            `'t'`: maximum flow kinetic energy, in :math:`J`.
-
-        Returns
-        -------
-        qoi_max_loc : numpy array
-            Consist of maximum value(s) of ``qoi`` at each location.
-            Shape of :code:`(nloc,)`.
-        """
-        warnings.warn(
-            "r.avaflow 2.4pre and lower versions are not supported by its \
-                developers, and their use is discouraged. Therefore, ravaflow24 \
-                module will be deprecated in the future versions. Please use \
-                ravaflow3G module instead.",
-            FutureWarning,
-        )
-
-        if not (loc.ndim == 2 and loc.shape[1] == 2):
-            raise ValueError(
-                "loc must be a 2d numpy array with first axis corresponding to"
-                " the number of locations and second axis to x and y coords"
-            )
-
-        if qoi not in ["h", "v", "p", "t"]:
-            raise ValueError("qoi must be 'h', 'v', 'p', or 't'")
-
-        qoi_max_raster_asc = os.path.join(
-            self.dir_sim,
-            f"{prefix}_results",
-            f"{prefix}_ascii",
-            f"{prefix}_{qoi}flow_max.asc",
-        )
-
-        header = [linecache.getline(qoi_max_raster_asc, i) for i in range(1, 6)]
-        header_values = [float(h.split()[-1].strip()) for h in header]
-        ncols, nrows, xll, yll, cellsize = header_values
-        ncols = int(ncols)
-        nrows = int(nrows)
-
-        x = np.arange(xll, xll + (cellsize * ncols), cellsize)
-        y = np.arange(yll, yll + (cellsize * nrows), cellsize)
-
-        if not all(
-            [
-                loc[i, 0] >= x[0]
-                and loc[i, 0] <= x[-1]
-                and loc[i, 1] >= y[0]
-                and loc[i, 1] <= y[-1]
-                for i in range(len(loc))
-            ]
-        ):
-            raise ValueError(
-                "Coordinates in loc must be within the boundary of topography"
-            )
-
-        qoi_max_raster = np.loadtxt(qoi_max_raster_asc, skiprows=6)
-        qoi_max_raster = np.rot90(np.transpose(qoi_max_raster))
-
-        f_qoi_max = interp2d(x, y, qoi_max_raster)
-
-        qoi_max_loc = [float(f_qoi_max(loc[i, 0], loc[i, 1])) for i in range(len(loc))]
-
-        return np.array(qoi_max_loc)
diff --git a/src/psimpy/simulator/ravaflow3G.py b/src/psimpy/simulator/ravaflow3G.py
index aff3d90f0607f660779b5b412a808373acd7cf06..d971537dc0c93425097783415e8c0351cb8d30b2 100644
--- a/src/psimpy/simulator/ravaflow3G.py
+++ b/src/psimpy/simulator/ravaflow3G.py
@@ -4,6 +4,7 @@ import numpy as np
 from scipy.interpolate import RegularGridInterpolator
 from typing import Union
 from beartype import beartype
+import warnings
 
 
 class Ravaflow3GMixture:
@@ -93,6 +94,12 @@ class Ravaflow3GMixture:
             `'0'`: Suppress change of direction induced by frictional or viscous forces (default).
             `'1'`: Do not suppress the change of direction.
         """
+        warnings.warn(
+            "r.avaflow 3 and lower versions are not supported by its \
+                developers, and their use is discouraged. Therefore, ravaflow3G \
+                module will be deprecated in the future versions.",
+            FutureWarning,
+        )
 
         if not os.path.isdir(dir_sim):
             raise ValueError(f"{dir_sim} does not exist or is not a directory")
@@ -203,6 +210,12 @@ class Ravaflow3GMixture:
             Name of the shell file (including path), which will be called by
             `GRASS <https://grass.osgeo.org/>`_ to run the simulation.
         """
+        warnings.warn(
+            "r.avaflow 3 and lower versions are not supported by its \
+                developers, and their use is discouraged. Therefore, ravaflow3G \
+                module will be deprecated in the future versions.",
+            FutureWarning,
+        )
 
         sh_file = os.path.join(self.dir_sim, f"{prefix}_shell.sh")
         grass_location = os.path.join(self.dir_sim, f"{prefix}_glocation")
@@ -275,6 +288,12 @@ class Ravaflow3GMixture:
         sh_file : str
             Name of the shell file (including path).
         """
+        warnings.warn(
+            "r.avaflow 3 and lower versions are not supported by its \
+                developers, and their use is discouraged. Therefore, ravaflow3G \
+                module will be deprecated in the future versions.",
+            FutureWarning,
+        )
         if not os.path.exists(grass_location):
             raise ValueError(f"{grass_location} does not exist")
         if not os.path.exists(os.path.join(grass_location, "PERMANENT")):
@@ -314,6 +333,12 @@ class Ravaflow3GMixture:
         impact_area : float
             A scalar value representing the overall impact area.
         """
+        warnings.warn(
+            "r.avaflow 3 and lower versions are not supported by its \
+                developers, and their use is discouraged. Therefore, ravaflow3G \
+                module will be deprecated in the future versions.",
+            FutureWarning,
+        )
 
         if qoi not in ["h", "v", "p", "t"]:
             raise ValueError("qoi must be 'h', 'v', 'p', or 't'")
@@ -361,6 +386,12 @@ class Ravaflow3GMixture:
         qoi_max : float or numpy array
             Maximum value(s) of ``qoi`` in one simulation.
         """
+        warnings.warn(
+            "r.avaflow 3 and lower versions are not supported by its \
+                developers, and their use is discouraged. Therefore, ravaflow3G \
+                module will be deprecated in the future versions.",
+            FutureWarning,
+        )
 
         if qoi not in ["h", "v", "p", "t"]:
             raise ValueError("qoi must be 'h', 'v', 'p', or 't'")
@@ -405,6 +436,12 @@ class Ravaflow3GMixture:
             Consist of maximum value(s) of ``qoi`` at each location.
             Shape of :code:`(nloc,)`.
         """
+        warnings.warn(
+            "r.avaflow 3 and lower versions are not supported by its \
+                developers, and their use is discouraged. Therefore, ravaflow3G \
+                module will be deprecated in the future versions.",
+            FutureWarning,
+        )
 
         if not (loc.ndim == 2 and loc.shape[1] == 2):
             raise ValueError(