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Standard -\begin_inset Note Note +\begin_layout Plain Layout +\begin_inset Float figure +placement document +alignment document +wide false +sideways false status open \begin_layout Plain Layout + +\end_layout + +\begin_layout Plain Layout +\begin_inset Graphics + filename Figures/Optimization/TunerConvergence.pdf + lyxscale 30 + width 60text% + +\end_inset + + +\begin_inset Caption Standard + +\begin_layout Plain Layout + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + \begin_inset Float figure placement document alignment document @@ -485,11 +531,15 @@ wide false sideways false status open +\begin_layout Plain Layout + +\end_layout + \begin_layout Plain Layout \begin_inset Graphics - filename Figures/InitialCondition.pdf + filename Figures/Optimization/TunerObjective.pdf lyxscale 30 - width 50text% + width 60text% \end_inset @@ -497,17 +547,34 @@ status open \begin_inset Caption Standard \begin_layout Plain Layout -Initial Condition + \end_layout \end_inset +\end_layout + +\begin_layout Plain Layout + +\end_layout + +\end_inset + + +\begin_inset Caption Standard + +\begin_layout Plain Layout + \end_layout \end_inset +\end_layout + +\begin_layout Plain Layout + \end_layout \end_inset @@ -515,6 +582,10 @@ Initial Condition \end_layout +\begin_layout Subsection +Reconstruction of the Solution +\end_layout + \begin_layout Standard \begin_inset Float figure placement document @@ -547,7 +618,22 @@ status open \begin_inset Caption Standard \begin_layout Plain Layout -Loss +The loss function +\begin_inset Formula $\Phi(\Theta)$ +\end_inset + + over the iterations plotted in a log-log plot. + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +What happens here? +\end_layout + +\end_inset + + \end_layout \end_inset diff --git a/Project3/src/Figures/Optimization/SingleSample/best_loss_theta.pdf 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b/Project3/src/HyperParameterOptimization.py index 10f09a7..9dc2b51 100644 --- a/Project3/src/HyperParameterOptimization.py +++ b/Project3/src/HyperParameterOptimization.py @@ -12,10 +12,10 @@ from MCMC import * #################################################################################################### # Setup #################################################################################################### -n_calls = 11 #!25 +n_calls = 25 # MCMC and solver parameters -MCMC_STEPS = 100#!500 +MCMC_STEPS = 300 #!500 MCMC_SUBSTEPS = 20 NUMBER_SAMPLES = 1 if NUMBER_SAMPLES == 1: diff --git a/Project3/src/InfluenceArtificialDiffusion.py b/Project3/src/InfluenceArtificialDiffusion.py new file mode 100644 index 0000000..e6f5c2b --- /dev/null +++ b/Project3/src/InfluenceArtificialDiffusion.py @@ -0,0 +1,99 @@ +import numpy as np +import matplotlib.pyplot as plt + +from MCMC import * + +ArtificialDiffusion = [1,2,3,4] +NUMBER_SAMPLES = 1 + +for art_diff in ArtificialDiffusion: + Theta, x_Theta, LOSS_THETA, LOSS_PHI, weights_historical = MCMC( + MCMC_STEPS=MCMC_STEPS, + MCMC_SUBSTEPS=MCMC_SUBSTEPS, + tau=tau, + beta=beta, + gamma=gamma, + k_i=k_i, + k_mu=k_mu, + k_sigma=k_sigma, + u_true=u_true, + number_samples=NUMBER_SAMPLES + ) + if NUMBER_SAMPLES == 1: + FigureFolder = 'Figures/SingleSample' + else: + FigureFolder = 'Figures/DoubleSample' + # Combine both loss functions + plt.figure() + plt.title('Losses') + plt.plot(LOSS_THETA[:], '--o', color='red', label='$\Phi(\Theta)$') + plt.plot(LOSS_PHI[:], '--o', color='green', label='$\Phi(\phi$)') + plt.xlabel('Iteration') + plt.ylabel('Loss') + plt.legend() + plt.grid() + plt.savefig(f'{FigureFolder}/losses.pdf', bbox_inches='tight') + plt.show() + + # Only the phi(theta) loss is plotted + plt.figure() + plt.title('Evolution of entropy loss') + plt.loglog(LOSS_THETA[:], '--o', color='red', label='$\Phi(\Theta)$') + plt.xlabel('Iteration') + plt.ylabel('$\Phi(\Theta)$') + plt.grid() + plt.savefig(f'{FigureFolder}/loss_theta.pdf', bbox_inches='tight') + plt.show() + + # Solve with the final Theta + t_vec, h_final = solve_PDE(Theta, T_end, NTime, x, dx, x_Theta, NUMBER_SAMPLES, M=M) + h_final = [extract_positions(t_vec[i], h_final[i], x) for i in range(NUMBER_SAMPLES)] + h_final = np.array([h_final[i].T for i in range(NUMBER_SAMPLES)]) + + colors = ['blue', 'red', 'green', 'purple'] + for sample in range(NUMBER_SAMPLES): + plt.figure() + plt.title(f'Predicted vs True - sample {sample+1}') + for i in range(4): + plt.plot([], [], color=colors[i], label=f'x = {x_observed[i]}') + plt.plot(times_observed, h_final[sample, i, :], color=colors[i]) + plt.plot(times_observed, u_true[i, :, sample], '--o', color=colors[i]) + plt.plot([], [], color='black', label='Predicted') + plt.plot([], [], '--o', color='black', label='True') + plt.xlabel('Time') + plt.ylabel('u(x,t)') + plt.legend(ncol=4, loc='upper center', bbox_to_anchor=(0.5, -0.1)) + plt.grid() + if NUMBER_SAMPLES == 1: + plt.savefig(f'{FigureFolder}/predicted_vs_true_single_sample.pdf', bbox_inches='tight') + else: + plt.savefig(f'{FigureFolder}/predicted_vs_true_both_samples_sample_{sample+1}.pdf', bbox_inches='tight') + plt.show() + + # Plot the final theta -> prediction for k(x) + plt.figure() + plt.title('Prediction for k(x)') + plt.plot(x_Theta, Theta, '--o', color='blue') + plt.xlabel('$x$') + plt.ylabel('$k(x)$') + plt.grid() + plt.savefig(f'{FigureFolder}/prediction_kx.pdf', bbox_inches='tight') + plt.show() + + # History of weights + plt.figure() + plt.title('History of weights') + marker = [':', '--'] + weights_historical = np.array(weights_historical) + for sample in range(NUMBER_SAMPLES): + for i in range(4*NUMBER_SAMPLES): + plt.plot(weights_historical[:,i], marker[sample], color=colors[i%4]) + plt.plot([], [], ':', color='black', label='Sample 1') + plt.plot([], [], '--', color='black', label='Sample 2') + [plt.plot([], [], color=colors[i], label=f'x = {x_observed[i%4]}') for i in range(4)] + plt.xlabel('Update Iteration') + plt.ylabel('Weight') + plt.legend() + plt.grid() + plt.savefig(f'{FigureFolder}/weights.pdf', bbox_inches='tight') + plt.show() \ No newline at end of file diff --git a/Project3/src/MCMC.py b/Project3/src/MCMC.py index 381e3b8..555c22e 100644 --- a/Project3/src/MCMC.py +++ b/Project3/src/MCMC.py @@ -58,7 +58,7 @@ def Upwind(u, M=M): F[-1] = f(u[-1]) return F -def solve_PDE(Theta, T_end, NTime, x, dx, x_Theta, number_samples=1, CFL=0.5, time_scheme='Euler'): +def solve_PDE(Theta, T_end, NTime, x, dx, x_Theta, number_samples=1, CFL=0.5, time_scheme='Euler', M=1): """ Solve the PDE u_t + (k(x) f(u))_x = 0, @@ -209,7 +209,7 @@ def MCMC( x_Theta = np.linspace(x0, x1, k_i+2) # Solve the PDE with the initial Theta - t_vec, h_Theta = solve_PDE(Theta, T_end, NTime, x, dx, x_Theta, number_samples) + t_vec, h_Theta = solve_PDE(Theta, T_end, NTime, x, dx, x_Theta, number_samples, M=M) h_Theta = np.array([extract_positions(t_vec[i], h_Theta[i], x) for i in range(number_samples)]).T h_Theta = h_Theta.flatten() dist_Theta = h_Theta - u_true_flatten @@ -226,7 +226,7 @@ def MCMC( Phi = np.sqrt(1 - beta**2) * Theta + beta * xi Phi[0], Phi[-1] = k_mu, k_mu - t_vec, h_Phi = solve_PDE(Phi, T_end, NTime, x, dx, x_Theta, number_samples) + t_vec, h_Phi = solve_PDE(Phi, T_end, NTime, x, dx, x_Theta, number_samples, M=M) h_Phi = np.array([extract_positions(t_vec[i], h_Phi[i], x) for i in range(number_samples)]).T h_Phi = h_Phi.flatten() dist_Phi = h_Phi - u_true_flatten @@ -264,7 +264,7 @@ def MCMC( Phi = np.sqrt(1 - beta**2) * Theta + beta * xi Phi[0], Phi[-1] = k_mu, k_mu - t_vec, h_Phi = solve_PDE(Phi, T_end, NTime, x, dx, x_Theta, number_samples) + t_vec, h_Phi = solve_PDE(Phi, T_end, NTime, x, dx, x_Theta, number_samples, M=M) h_Phi = np.array([extract_positions(t_vec[i], h_Phi[i], x) for i in range(number_samples)]).T h_Phi = h_Phi.flatten() dist_Phi = h_Phi - u_true_flatten @@ -345,7 +345,7 @@ if __name__ == '__main__': plt.show() # Solve with the final Theta - t_vec, h_final = solve_PDE(Theta, T_end, NTime, x, dx, x_Theta, NUMBER_SAMPLES) + t_vec, h_final = solve_PDE(Theta, T_end, NTime, x, dx, x_Theta, NUMBER_SAMPLES, M=M) h_final = [extract_positions(t_vec[i], h_final[i], x) for i in range(NUMBER_SAMPLES)] h_final = np.array([h_final[i].T for i in range(NUMBER_SAMPLES)]) diff --git a/Project3/src/data/TunerResults.npz b/Project3/src/data/TunerResults.npz deleted file mode 100644 index 43e6d2932c9f521ca735f5c6f0bce4af6c675854..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1336 zcmWIWW@gc4fB;2?oVD@R|Dk}JL4+YMJ~=Tbr&uqqppub6fT07T4o*+@3-t|%WMn8~ zs8&x&Elw^{w^C5I$+S?{QBY6IFDfZY%!|)2N=XHYyCvonr|KxE7iT0Eq^esfXlUvv z)GAN}xVWM2LG?s&!IvzkAO7<(h%h9j7MH}Q78T_ek>-yyy7|L!!IFOyR=PT%`s4SH znpT)Ugkk<DNGwXsO)W_+f=9{(Xdu97?2$sGXN+_xjTWw{rB}G6c6ZoE$gkdWwDN*I zs;8bbhl#>G#S8OPQff)!V2vA?cTl~-GWDJ;%o_q=Z<Hj)XU7+3rsob?pCBTHkx7>s zHPeG~HVDIV6evwKFoH;=A|SvURU;^)fi!_IA4n|}H!vP$U_i@u=z2kk8<b)}SQx4g 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Tuner Results and Timings ... -... Tuner results ... -n_calls: 11 -Best error: 43.32473738706938 -Best parameters: [0.012075618253727419, 0.25743239807751683] -Best beta: 0.012075618253727419 -Best k_sigma: 0.25743239807751683 diff --git a/Project3/src/data/TunerResultsSingleSample.txt.npz b/Project3/src/data/TunerResultsSingleSample.txt.npz new file mode 100644 index 0000000000000000000000000000000000000000..e2eeb0d83c588ee6660d7588e70a22d3685a3604 GIT binary patch literal 1854 zcmWIWW@gc4fB;1XtJw!x|3d*cg9t-jd~#w=PO)BIK_w%D07C~v9h{!*7wQ`j$;eQ~ zP_3SlTAW;@Zl$1ZlWC!@qoAIaUsO_*m=~X4l#&V(cT3DEPSsIRFV09TNL9B|(9qOT zs8yf{a7jYlgX)RH-wby`{qUcUL4+YGwYVfcwWuh+h%|qs(aj%ATt7N|{3PUn>W^0S zeKTSH5Qh1qAh9ShH?<_S2p%aDpn(9Ru}2D#o-xv)G+MZ>9f}Cs_Mp%HMe%=0ZRacY zsGcg<$UG186fewENvS1?gEeko-a++7&6;bMVcrk`d!r;VK0CfRGd*|E`UHD~u${dB z7v>XCZVAaqElG^eO-;-jtTA$jYsX9fj(2DYtK;)rA(%fv2@B$n;*ylX>Wx(?{c^QW z&)5feGcxHiqn5#-f)<3ip?MobH86rmq!JljBdFX1X#!zBkXk5iU_8pefL02k>jjlH zpaKMhg`xUDR0Cr#BUCSH$%AeHC|`pt24P;1PAG0*Ok#o>0L$g*T0waUqz!}xpxQuG z1EVH0NGod2Le~vSzaX6;jOy#p%nS^WQ~*oO=z2kE2BZ&!Q60UT1*R98f&#o**+7nB QXJBVo#>l|X#0ug80Hpe?v;Y7A literal 0 HcmV?d00001 diff --git a/Project3/src/data/TunerResultsSingleSample.txt.txt b/Project3/src/data/TunerResultsSingleSample.txt.txt new file mode 100644 index 0000000..842b8c3 --- /dev/null +++ b/Project3/src/data/TunerResultsSingleSample.txt.txt @@ -0,0 +1,10 @@ +... Tuner Results and Timings ... +... Tuner results ... +n_calls: 25 +Best error: 4.737248434759213 +Best parameters: [0.015077042112439026, 0.31659963168004746] +Best beta: 0.015077042112439026 +Best k_sigma: 0.31659963168004746 +... Statistics of Theta ... +Mean of Theta: 0.9541396679709027 +Standard deviation of Theta: 0.2257534407824882 -- GitLab