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Commit aea7255c authored by Jan Habscheid's avatar Jan Habscheid
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Euler in Deepxde

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ExplicitEulerPINN/DeepXDE.ipynb 0 → 100644
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%% Cell type:code id: tags:
``` python
import deepxde as dde
from deepxde.backend import tf
import tensorflow as tf_flow
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d
# Import your physical coefficient functions
from HeatCoefficients import *
```
%% Cell type:code id: tags:
``` python
import deepxde as dde
import numpy as np
import tensorflow as tf
from scipy.interpolate import interp1d
# Define spatial domain
geom = dde.geometry.Interval(0, 1)
# Discretized time steps
time_steps = np.linspace(0, .1, 3) # Example: 100 time steps
# Define boundary conditions
def boundary_l(x, on_boundary):
return on_boundary and np.isclose(x[0], 0)
def boundary_r(x, on_boundary):
return on_boundary and np.isclose(x[0], 1)
bc_l = dde.DirichletBC(
geom,
lambda x: 0,
boundary_l
)
bc_r = dde.DirichletBC(
geom,
lambda x: 1,
boundary_r
)
# Initialize previous solution
x_train = np.linspace(0, 1, 1001)[:, None]
prev_solution_values = np.zeros_like(x_train) # Initial condition T(x,0) = 0
prev_solution = interp1d(x_train.flatten(), prev_solution_values.flatten(), kind="linear", fill_value="extrapolate")
models_trained = []
for n in range(1, len(time_steps)):
t_n = time_steps[n]
t_prev = time_steps[n-1]
dt = t_n - t_prev
# Define PDE residual for the time step using explicit time-stepping
def pde(x, u):
u_xx = dde.grad.hessian(u, x, i=0, j=0) # Second spatial derivative
# Interpolate previous solution (x is a Tensor -> use x.numpy() in NumPy)
u_prev_tf = tf.py_function(func=lambda x: prev_solution(x.numpy()), inp=[x[:, 0:1]], Tout=tf.float32)
if n==1:
u_prev_tf = tf.constant(0.0, shape=(x.shape[0], 1), dtype=tf.float32)
u_t = (u - u_prev_tf) / dt # Explicit time difference
return u_t - .4 * u_xx # Heat equation: u_t = u_xx
# Define training data by sampling from the previous time step
y_train = prev_solution(x_train) # Get previous time step's solution
# Define the dataset for this time step
data = dde.data.PDE(
geom,
pde,
[bc_l, bc_r],
num_domain=1000,
num_boundary=50,
)
# Define and train the model
net = dde.nn.FNN(
[1] + [32] * 3 + [1],
"tanh",
"Glorot uniform"
)
net.apply_output_transform(lambda x, y: x + x * (1 - x) * y) # Enforce boundary conditions
model = dde.Model(data, net)
model.compile(
"adam",
lr=0.001
)
model.train(epochs=5000)
# Store the trained model output for the next time step
prev_solution_values = model.predict(x_train)
# Update interpolator for next step
prev_solution = interp1d(x_train.flatten(), prev_solution_values.flatten(), kind="linear", fill_value="extrapolate")
models_trained.append(model)
# Final model is the last trained model
```
%% Output
Compiling model...
'compile' took 0.001537 s
Warning: epochs is deprecated and will be removed in a future version. Use iterations instead.
Training model...
WARNING:tensorflow:AutoGraph could not transform <function <lambda> at 0x31160cea0> and will run it as-is.
Cause: could not parse the source code of <function <lambda> at 0x31160cea0>: no matching AST found among candidates:
# coding=utf-8
lambda x, on: np.array([on_boundary(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary1(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary2(x[i], on[i]) for i in range(len(x))])
To silence this warning, decorate the function with @tf.autograph.experimental.do_not_convert
WARNING: AutoGraph could not transform <function <lambda> at 0x31160cea0> and will run it as-is.
Cause: could not parse the source code of <function <lambda> at 0x31160cea0>: no matching AST found among candidates:
# coding=utf-8
lambda x, on: np.array([on_boundary(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary1(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary2(x[i], on[i]) for i in range(len(x))])
To silence this warning, decorate the function with @tf.autograph.experimental.do_not_convert
WARNING:tensorflow:AutoGraph could not transform <function <lambda> at 0x31160d120> and will run it as-is.
Cause: could not parse the source code of <function <lambda> at 0x31160d120>: no matching AST found among candidates:
# coding=utf-8
lambda x, on: np.array([on_boundary(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary1(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary2(x[i], on[i]) for i in range(len(x))])
To silence this warning, decorate the function with @tf.autograph.experimental.do_not_convert
WARNING: AutoGraph could not transform <function <lambda> at 0x31160d120> and will run it as-is.
Cause: could not parse the source code of <function <lambda> at 0x31160d120>: no matching AST found among candidates:
# coding=utf-8
lambda x, on: np.array([on_boundary(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary1(x[i], on[i]) for i in range(len(x))])
# coding=utf-8
lambda x, on: np.array([on_boundary2(x[i], on[i]) for i in range(len(x))])
To silence this warning, decorate the function with @tf.autograph.experimental.do_not_convert
Step Train loss Test loss Test metric
0 [1.74e+02, 0.00e+00, 0.00e+00] [1.74e+02, 0.00e+00, 0.00e+00] []
1000 [5.80e-02, 0.00e+00, 0.00e+00] [5.80e-02, 0.00e+00, 0.00e+00] []
2000 [5.58e-03, 0.00e+00, 0.00e+00] [5.58e-03, 0.00e+00, 0.00e+00] []
3000 [2.12e-03, 0.00e+00, 0.00e+00] [2.12e-03, 0.00e+00, 0.00e+00] []
4000 [1.10e-03, 0.00e+00, 0.00e+00] [1.10e-03, 0.00e+00, 0.00e+00] []
5000 [1.54e-02, 0.00e+00, 0.00e+00] [1.54e-02, 0.00e+00, 0.00e+00] []
Best model at step 4000:
train loss: 1.10e-03
test loss: 1.10e-03
test metric: []
'train' took 9.123625 s
Compiling model...
'compile' took 0.000856 s
Warning: epochs is deprecated and will be removed in a future version. Use iterations instead.
Training model...
Step Train loss Test loss Test metric
0 [8.90e+01, 0.00e+00, 0.00e+00] [8.90e+01, 0.00e+00, 0.00e+00] []
1000 [9.23e-01, 0.00e+00, 0.00e+00] [9.23e-01, 0.00e+00, 0.00e+00] []
2000 [9.05e-01, 0.00e+00, 0.00e+00] [9.05e-01, 0.00e+00, 0.00e+00] []
3000 [1.46e-03, 0.00e+00, 0.00e+00] [1.46e-03, 0.00e+00, 0.00e+00] []
4000 [9.36e-05, 0.00e+00, 0.00e+00] [9.36e-05, 0.00e+00, 0.00e+00] []
5000 [5.56e-05, 0.00e+00, 0.00e+00] [5.56e-05, 0.00e+00, 0.00e+00] []
Best model at step 5000:
train loss: 5.56e-05
test loss: 5.56e-05
test metric: []
'train' took 9.123659 s
%% Cell type:code id: tags:
``` python
x_evaluate = np.linspace(0, 1, 101).reshape(-1, 1)
for model in models_trained:
y_evaluate = model.predict(x_evaluate)
plt.plot(x_evaluate, y_evaluate)
plt.legend()
plt.grid()
plt.show()
```
%% Output
/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_18655/3937913252.py:5: UserWarning: No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
plt.legend()
InitFEniCS/Tuner_InitFenicsx.ipynb
+ 6382
− 7410
View file @ aea7255c
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