def eta_histogram(results_path, save_path, prefix, train, labels):
"""
Histogram of samples by individual sample eta.
"""
plt.clf()
n_class = len(labels)
colors = sns.cubehelix_palette(n_class, start=2, rot=0, dark=0, light=.5)
plt.figure(figsize=(6, 6))
etas = np.array(load_results(
results_path, f"{prefix}_pca20.json")["etas"])
targets = train["targets"].numpy()
etas = [etas[targets == c] for c in range(n_class)]
for c in range(n_class):
plt.hist(
etas[c], bins=80, color=colors[c], alpha=0.5, label=f"{labels[c]}")
plt.axvline(
etas[c].mean(), color=colors[c], linestyle='dashed', linewidth=2)
plt.xlabel("Per sample $\eta$", fontsize=30)
plt.xticks(fontsize=26)
plt.ylabel("Number of samples", fontsize=30)
plt.yticks(fontsize=26)
plt.legend()
plotting.savefig(os.path.join(save_path, f"{prefix}_eta_hist"))
def VisuError(Error, testcases, Savetofile=False):
name = testcases.name
Vals = testcases.Vals
symbols = ('^','o', 's','D','p','H',)
lines = ('-', '--',':', '-.','.',)
newfig(width=1.3)
for i in range(len(Vals)):
namestr = ', ' + '$N_s$=' + str(Vals[i])
if name != 'SampleNum' and i ==0:
plt.semilogy(M_Vec,Error[i,:,4], 'k-.',label='Projection' )
plt.semilogy(M_Vec,Error[i,:,0], 'r-.',label='POD-G ' )
elif name == 'SampleNum':
plt.semilogy(M_Vec,Error[i,:,4], 'k-.'+symbols[i] ,label='Projection'+namestr )
plt.semilogy(M_Vec,Error[i,:,0], 'r-.'+symbols[i] ,label='POD-G' +namestr )
if not( name == 'NResi' ):
plt.semilogy(M_Vec,Error[i,:,1], 'y:'+symbols[i] ,label='PDNN' +namestr )
plt.semilogy(M_Vec,Error[i,:,2], 'g--'+symbols[i] ,label='PINN'+namestr )
plt.semilogy(M_Vec,Error[i,:,3], 'g-'+symbols[i] ,label='PRNN'+namestr )
plt.xlabel('$m$')
plt.ylabel('Error')
#plt.title(name)
plt.legend(loc="lower left", ncol=1, handlelength=3)
plt.show()
if Savetofile:
savefig("fig/ErrorComparsion_"+name)
def view_images(train, results_path, save_path, prefix):
"""
View the most and least leaked images.
"""
# sort etas by index
etas = load_results(
results_path, f"{prefix}_pca20.json")["etas"]
sorted_etas = sorted(
zip(etas, range(len(etas))), key=lambda x: x[0], reverse=True)
ims = train["features"].squeeze()
n_ims = 8
f, axarr = plt.subplots(2, n_ims, figsize=(7, 2.2))
f.subplots_adjust(wspace=0.05)
for priv in [False, True]:
for i in range(n_ims):
ax = axarr[int(priv), i]
idx = -(i + 1) if priv else i
im = sorted_etas[idx][1]
image = ims[im, ...]
if image.ndim == 3:
image = image.permute(1, 2, 0)
ax.imshow(image, cmap='gray')
ax.axis("off")
title = "{:.1e}".format(sorted_etas[idx][0])
ax.set_title(title, fontsize=14)
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
plotting.savefig(os.path.join(save_path, f"{prefix}_images"))
plt.close(f)
def save_bigprofiles(prots, protids, unnorm_eluts, fname, hires_mult=1, **kwargs):
import plotting as pl
nplots = plot_bigprofiles(prots, protids, unnorm_eluts, **kwargs)
fig = pl.gcf()
nprots = len(prots) if prots else len(protids)
fig.set_size_inches(20, 4+(nplots/4)*nprots)
pl.savefig(fname, bbox_inches='tight', dpi=200*hires_mult)
pl.clf()
def VisuError(Error, testcases, Savetofile=False):
name = testcases.name
Vals = testcases.Vals
symbols = ('^','o', 's','D','p','H',)
lines = ('-', '--',':', '-.','.',)
#plt.close('all')i
if name == 'SampleNum':
tmp = '$N_s$'
width = 1.3
elif name =='NetSize':
tmp = '$n_H$'
width = 1
elif name == 'NResi':
tmp = '$N_{Resi}$'
width = 1
newfig(width=width)
for i in range(len(Vals)):
namestr = ', ' + tmp+'=' + str(Vals[i])
if name != 'SampleNum' and i ==0:
plt.semilogy(M_Vec,Error[i,:,4], 'k-.',label='Projection' )
plt.semilogy(M_Vec,Error[i,:,0], 'r-.',label='POD-G ' )
elif name == 'SampleNum':
plt.semilogy(M_Vec,Error[i,:,4], 'k-.'+symbols[i] ,label='Projection'+namestr )
plt.semilogy(M_Vec,Error[i,:,0], 'r-.'+symbols[i] ,label='POD-G' +namestr )
if not( name == 'NResi' ):
plt.semilogy(M_Vec,Error[i,:,1], 'y:'+symbols[i] ,label='PDNN' +namestr )
plt.semilogy(M_Vec,Error[i,:,2], 'g--'+symbols[i] ,label='PINN'+namestr )
plt.semilogy(M_Vec,Error[i,:,3], 'g-'+symbols[i] ,label='PRNN'+namestr )
if name == 'NResi':
plt.ylim(bottom=9E-5)
elif name == 'NetSize':
plt.ylim(bottom=7E-5)
plt.xlabel('$m$')
plt.ylabel(r'Error $\varepsilon$')
#plt.title(name)
plt.legend(loc="lower left", ncol=1, handlelength=3)
if name == 'NResi':
plt.legend(loc="best", ncol=1, handlelength=3)
plt.show()
if Savetofile:
savefig("fig/ErrorComparsion_"+name)
def __init__(self, parent, controller):
tk.Frame.__init__(self, parent)
self.controller = controller
self.x_name = tk.StringVar()
self.y_name = tk.StringVar()
self.x_data = tk.StringVar()
self.y_data = tk.StringVar()
tk.Button(self,
text="Back",
command=lambda: controller.show_frame("PageOne")).grid(
column=0, row=0, sticky="W")
self.plotbutton = tk.Button(
self,
text="Plot",
command=lambda: fitAndPlot(PageOne.data[self.x_data.get()], PageOne
.data[self.y_data.get()]))
PageOne.data = {
"a": ((1, 2, 3, 4), (1, 1, 1, 1)),
"b": ((2, 4, 5, 6), (1, 1, 1, 1))
}
tk.Button(self, text="more plot",
command=lambda: self.makePlot()).grid(column=0,
row=1,
sticky="W")
self.plotbutton.grid(column=0, row=2, sticky="W")
tk.Entry(self, textvariable=self.x_name).grid(column=1, row=3)
tk.Entry(self, textvariable=self.y_name).grid(column=1, row=4)
tk.Entry(self, textvariable=self.x_data).grid(column=1, row=5)
tk.Entry(self, textvariable=self.y_data).grid(column=1, row=6)
tk.Label(self, text="x Name").grid(column=0, row=3, sticky="W")
tk.Label(self, text="y Name").grid(column=0, row=4, sticky="W")
tk.Label(self, text="x Data").grid(column=0, row=5, sticky="W")
tk.Label(self, text="x Data").grid(column=0, row=6, sticky="W")
tk.Button(self, text="save",
command=lambda: savefig(self.fig)).grid(column=0, row=7)
self.option_menu_y = tk.OptionMenu(self, self.x_data,
*PageOne.data.keys())
self.option_menu_y.grid(column=0, row=8)
self.variable = tk.StringVar()
PlotPage.menu_y = self.option_menu_y["menu"]
PlotPage.menu_y.add(
"command",
label="test",
command=lambda value="test": self.x_data.set("test"))
"""
while True:
self.option_menu_y.grid_forget()
self.option_menu_y = tk.OptionMenu(self, self.x_data, PageOne.data.keys())
self.option_menu_y.grid(column=0, row=8)
t.sleep(5)
"""
"""
def correlations(results_path, save_path, prefix):
results = load_results(results_path, f"{prefix}_pca20.json")
etas = np.array(results["etas"])
n_samples = 2000
np.random.seed(n_samples)
samples = np.random.permutation(len(etas))[:n_samples]
losses = np.array(results["train_losses"])
grad_norms = np.array(results["train_grad_norms"])
alternatives = [
("loss", "(a) Loss $\ell({\\bf w^*}^\\top {\\bf x}, y)$", losses),
("gradnorm", "(b) Gradient norm $\|\\nabla_{\\bf w^*} \ell\|_2$", grad_norms)]
f, axarr = plt.subplots(1, 2, figsize=(10, 4), sharey=True)
f.subplots_adjust(wspace=0.1)
for e, (method, xlabel, values) in enumerate(alternatives):
ax = axarr[e]
ax.scatter(values[samples], etas[samples], s=2.5, color=COLOR)
ax.set_xlabel(xlabel)
axarr[0].set_ylabel("FIL $\eta$")
plotting.savefig(os.path.join(save_path, f"{prefix}_scatter_alternatives_eta"))
plt.clf()
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Exact $D(t,x)$', fontsize=10)
######## Learned d(t,x,y) ###########
ax = plt.subplot(gs[1:2, 1])
h = plot_solution(t, x, d_pred, ax)
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Learned $D(t,x)$', fontsize=10)
savefig('./figures/turbulence_1D_diffusion', crop=False)
scipy.io.savemat(
'turbulence_1D_diffusion_results_%s.mat' % (time.strftime('%d_%m_%Y')),
{
't': t,
'x': x,
'u': u,
'd': d,
'u_pred': u_pred,
'd_pred': d_pred
})
ax.set_title('$t = 0.50$', fontsize = 10)
ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.35), ncol=5, frameon=False)
ax = plt.subplot(gs1[0, 2])
ax.plot(x,Exact[75,:], 'b-', linewidth = 2, label = 'Exact')
ax.plot(x,U_pred[75,:], 'r--', linewidth = 2, label = 'Prediction')
ax.set_xlabel('$x$')
ax.set_ylabel('$u(t,x)$')
ax.axis('square')
ax.set_xlim([-1.1,1.1])
ax.set_ylim([-1.1,1.1])
ax.set_title('$t = 0.75$', fontsize = 10)
####### Row 3: Identified PDE ##################
gs2 = gridspec.GridSpec(1, 3)
gs2.update(top=1.0-2.0/3.0, bottom=0, left=0.0, right=1.0, wspace=0.0)
ax = plt.subplot(gs2[:, :])
ax.axis('off')
s1 = r'$\begin{tabular}{ |c|c| } \hline Correct PDE & $u_t + u u_x - 0.0031831 u_{xx} = 0$ \\ \hline Identified PDE (clean data) & '
s2 = r'$u_t + %.5f u u_x - %.7f u_{xx} = 0$ \\ \hline ' % (lambda_1_value, lambda_2_value)
s3 = r'Identified PDE (1\% noise) & '
s4 = r'$u_t + %.5f u u_x - %.7f u_{xx} = 0$ \\ \hline ' % (lambda_1_value_noisy, lambda_2_value_noisy)
s5 = r'\end{tabular}$'
s = s1+s2+s3+s4+s5
ax.text(0.1,0.1,s)
'''
savefig('./figures/NGSIM_infer')
print("number of loops:", Loop_Num)
######## Exact solution #######################
######## Predicted p(t,x,y) ###########
gs = gridspec.GridSpec(1, 2)
gs.update(top=0.8, bottom=0.2, left=0.1, right=0.9, wspace=0.5)
ax = plt.subplot(gs[:, 0])
h = ax.imshow(Exact_idn, interpolation='nearest', cmap='jet',
extent=[lb_idn[0], ub_idn[0]*keep, lb_idn[1], ub_idn[1]],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Exact Dynamics', fontsize = 10)
######## Approximation Error ###########
ax = plt.subplot(gs[:, 1])
h = ax.imshow(abs(Exact_idn-U_pred), interpolation='nearest', cmap='jet',
extent=[lb_idn[0], ub_idn[0]*keep, lb_idn[1], ub_idn[1]],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Identifier Error', fontsize = 10)
savefig('Results/KdV_idn_relu')
interpolation='nearest',
cmap='jet',
extent=[lb_idn[0], ub_idn[0] * keep, lb_idn[1], ub_idn[1]],
origin='lower',
aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Exact Dynamics', fontsize=10)
######## Approximation Error ###########
ax = plt.subplot(gs[:, 1])
h = ax.imshow(abs(Exact_idn - U_pred),
interpolation='nearest',
cmap='jet',
extent=[lb_idn[0], ub_idn[0] * keep, lb_idn[1], ub_idn[1]],
origin='lower',
aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Identifier Error', fontsize=10)
savefig('Results/KdV_idn_rat')
Y_test[0:1, -1, 0],
'ko',
label='$Y_T = u(T,X_T)$')
plt.plot(t_test[1:samples, :, 0].T, Y_pred[1:samples, :, 0].T, 'b')
plt.plot(t_test[1:samples, :, 0].T, Y_test[1:samples, :, 0].T, 'r--')
plt.plot(t_test[1:samples, -1, 0], Y_test[1:samples, -1, 0], 'ko')
plt.plot([0], Y_test[0, 0, 0], 'ks', label='$Y_0 = u(0,X_0)$')
plt.xlabel('$t$')
plt.ylabel('$Y_t = u(t,X_t)$')
plt.title('100-dimensional Black-Scholes-Barenblatt')
plt.legend()
savefig('BSB.png', crop=False)
errors = np.sqrt((Y_test - Y_pred)**2 / Y_test**2)
mean_errors = np.mean(errors, 0)
std_errors = np.std(errors, 0)
plt.figure()
plt.plot(t_test[0, :, 0], mean_errors, 'b', label='mean')
plt.plot(t_test[0, :, 0],
mean_errors + 2 * std_errors,
'r--',
label='mean + two standard deviations')
plt.xlabel('$t$')
plt.ylabel('relative error')
plt.title('100-dimensional Black-Scholes-Barenblatt')
plt.legend()
interpolation='nearest',
cmap='jet',
extent=[lb_idn[0], ub_idn[0] * keep, lb_idn[1], ub_idn[1]],
origin='lower',
aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Exact Dynamics', fontsize=10)
######## Approximation Error ###########
ax = plt.subplot(gs[:, 1])
h = ax.imshow(abs(Exact_idn - U_pred),
interpolation='nearest',
cmap='jet',
extent=[lb_idn[0], ub_idn[0] * keep, lb_idn[1], ub_idn[1]],
origin='lower',
aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Identifier Error', fontsize=10)
savefig('Results/Rational_%d_%d/KdV_idn_rat' % (rP, rQ))
t = f['t']
# read yml file
yml_path = files.find(args[0], 'yml')
ps = yaml.load(open(yml_path).read())
plmat = ps['plot_matrix'] if 'plot_matrix' in ps else None
if save:
files.delete_images()
# show/save a graph for every connection
# or a single graph if plot_matrix is specified
if plmat:
conns = {}
for n in nodes:
conns[n.name] = {}
for c in connections:
conns[c.origin_node.name][c.dest_node.name] = c
pl.plot_matrix(plmat, conns, t)
if save:
pl.savefig(files.image_path())
else:
for c in connections:
pl.plot_connection(c, t)
if save:
pl.savefig(files.image_path(c))
if not save:
pl.show()
gs = gridspec.GridSpec(1, 1)
gs.update(top=0.9, bottom=0.1, left=0.1, right=0.9, wspace=0.7, hspace=0.5)
# ######## Exact solution #######################
ax = plt.subplot(gs[0, 0])
h = ax.imshow(Exact_idn,
interpolation='nearest',
cmap='jet',
extent=[lb_idn[0], ub_idn[0], lb_idn[1], ub_idn[1]],
origin='lower',
aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
savefig('Results/solution')
fig, ax = newfig(2.0, 0.5)
ax.axis('off')
gs = gridspec.GridSpec(1, 3)
gs.update(top=0.9, bottom=0.1, left=0.1, right=0.9, wspace=0.5)
######## ReLU error #######################
ax = plt.subplot(gs[0, 0])
h = ax.imshow(abs(Exact_idn - U_relu),
interpolation='nearest',
cmap='jet',
extent=[lb_idn[0], ub_idn[0], lb_idn[1], ub_idn[1]],
origin='lower',
aspect='auto',
vmin=0.0,
f.write("% Automatically generated\n")
f.write("\\newcommand{{\\accfrac}}{{{0:.2f}}}\n".format(acc_frac))
f.write("\\newcommand{{\\taua}}{{{0:.0f}}}\n".format(tau[0]))
f.write("\\newcommand{{\\taub}}{{{0:.0f}}}\n".format(tau[1]))
# Plot the traces and corner plot.
fig, axes = plt.subplots(2, 1, figsize=SQUARE_FIGSIZE, sharex=True)
axes[0].plot(chain[:5000, 0], "k")
axes[1].plot(chain[:5000, 1], "k")
axes[0].set_ylabel(r"$\theta_1$")
axes[1].set_ylabel(r"$\theta_2$")
axes[1].set_xlabel("step")
axes[0].yaxis.set_major_locator(plt.MaxNLocator(4))
axes[1].yaxis.set_major_locator(plt.MaxNLocator(4))
axes[1].xaxis.set_major_locator(plt.MaxNLocator(3))
savefig(fig, "traces.pdf")
plt.close(fig)
fig = corner.corner(chain, labels=[r"$\theta_1$", r"$\theta_2$"])
savefig(fig, "corner.pdf")
plt.close(fig)
fig, ax = plt.subplots(1, 1, figsize=SQUARE_FIGSIZE, sharex=True)
p = autocorr.function(chain)
ax.plot(p[:, 0], label=r"$f(\theta) = \theta_1$")
ax.plot(p[:, 1], label=r"$f(\theta) = \theta_2$")
p = autocorr.function(np.prod(chain, axis=1))
ax.plot(p, label=r"$f(\theta) = \theta_1 \, \theta_2$")
ax.set_title("Metropolis")
ax.set_ylabel("autocorrelation")
ax.set_xlabel("lag [steps]")
h = plot_solution(t, x, d, ax)
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Exact $D(t,x)$', fontsize=10)
######## Learned d(t,x,y) ###########
ax = plt.subplot(gs[1:2, 1])
h = plot_solution(t, x, d_pred, ax)
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Learned $D(t,x)$', fontsize=10)
savefig('./figures/Results_1D', crop=False)
scipy.io.savemat('turbulence_results_%s.mat' % (time.strftime('%d_%m_%Y')),
{
't': t,
'x': x,
'u': u,
'd': d,
'u_pred': u_pred,
'd_pred': d_pred
})
ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.35), ncol=5, frameon=False)
ax = plt.subplot(gs1[0, 2])
ax.plot(x,Exact[75,:], 'b-', linewidth = 2, label = 'Exact')
ax.plot(x,U_pred[75,:], 'r--', linewidth = 2, label = 'Prediction')
lower = U_pred[75,:] - 2.0*np.sqrt(Sigma_pred[75,:])
upper = U_pred[75,:] + 2.0*np.sqrt(Sigma_pred[75,:])
plt.fill_between(x.flatten(), lower.flatten(), upper.flatten(),
facecolor='orange', alpha=0.5, label="Two std band")
ax.set_xlabel('$x$')
ax.set_ylabel('$u(t,x)$')
ax.axis('square')
ax.set_xlim([-1.1,1.1])
ax.set_ylim([-1.1,1.1])
ax.set_title('$t = 0.75$', fontsize = 10)
savefig('./Prediction')
fig, ax = newfig(1.0)
ax.axis('off')
############# Uncertainty ##################
gs2 = gridspec.GridSpec(1, 2)
gs2.update(top=1-0.06, bottom=1-1/3, left=0.15, right=0.85, wspace=0)
ax = plt.subplot(gs2[:, :])
h = ax.imshow(Sigma_pred.T, interpolation='nearest', cmap='rainbow',
extent=[t.min(), t.max(), x.min(), x.max()],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
# Plot the different solutions
fig, ax = newfig(0.6, 1.2)
ax.axis('off')
gs = gridspec.GridSpec(1, 1)
gs.update(top=0.9, bottom=0.1, left=0.1, right=0.9, wspace=0.7, hspace=0.5)
# ######## Exact solution #######################
ax = plt.subplot(gs[0, 0])
h = ax.imshow(Exact_idn, interpolation='nearest', cmap='jet',
extent=[lb_idn[0], ub_idn[0], lb_idn[1], ub_idn[1]],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
savefig('Results/solution')
fig, ax = newfig(2.0, 0.5)
ax.axis('off')
gs = gridspec.GridSpec(1, 3)
gs.update(top=0.9, bottom=0.1, left=0.1, right=0.9, wspace=0.5)
######## ReLU error #######################
ax = plt.subplot(gs[0, 0])
h = ax.imshow(abs(Exact_idn-U_relu), interpolation='nearest', cmap='jet',
extent=[lb_idn[0], ub_idn[0], lb_idn[1], ub_idn[1]],
origin='lower', aspect='auto', vmin=0.0, vmax=0.05)
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
# of weights and biases.
model = PINN(x_train, t_train, rho_train, u_train, p_train, E_train, layers)
model.train(20000)
#model.train2(num_epochs = 200, batch_size = 10000, learning_rate=1e-3)
#model.train2(num_epochs = 300, batch_size = 10000, learning_rate=1e-4)
#model.train2(num_epochs = 300, batch_size = 10000, learning_rate=1e-5)
#model.train2(num_epochs = 200, batch_size = 10000, learning_rate=1e-6)
# Plotting Loss
plt.plot(loss_vector, label='Loss value')
plt.legend()
plt.title('Loss value over iterations')
plt.xlabel('Iterations')
plt.ylabel('Loss')
savefig('./figures/Loss', crop = False)
plt.show()
# Test Data
# Test the neural network performance using Test dataset "data1" generated
# by eliminating the initally randomly selected rows from the data. The test
# dataset "data1" is then sliced to get test parameter values.
data1 = data
data1 = np.delete(data1, idx, 0)
print(data.shape)
# x
x_test = data1[:,0:1].flatten()[:,None]
t_test = data1[:,1:2].flatten()[:,None]
XT_test = np.concatenate([x_test, t_test], 1)
# y
random_state = np.random.RandomState(seed=0)
states = np.arange(7)
weights = np.array([1, 1, 1, 1, 1, 1, 10, 1])
alpha = 0.01
gamma = 0.99
weights_list = [weights]
for i in range(n_steps):
s = random_state.choice(states)
weights = weights + 7 * alpha * (gamma * q(states[-1], weights) -
q(s, weights)) * feature(s)
weights_list.append(weights)
output = np.c_[weights_list]
with plt.rc_context(plotting.rc()):
fig, ax = plt.subplots(1)
lines = ax.plot(output)
ax.legend(lines, [f"w{i+1}" for i in range(output.shape[1])])
ax.grid(alpha=0.1)
ax.set_xlabel("Steps")
ax.set_ylabel("Weight")
ax.set_title("Q-learning on Baird's Counterexample")
plt.tight_layout()
plotting.savefig(fig,
path=os.path.join(
c.Paths.output, "ex_11_3",
"bairds_counter_example_q_learning.png"))
return self.loss_Eqs(x, self.u_net(x), source, weight)
def loss_Eqs(self, x, lamda, source, weight=1):
# def loss_PINN(self,x,source):
#lamda = self.u_net(x);
fx = torch.matmul(lamda[:, None, None, :], self.A[None, :, :, :])
fx = torch.matmul(fx, lamda[:, None, :, None])
fx = fx.view(lamda.shape)
fx = fx + torch.matmul(lamda, self.B.T) - source
return self.lossfun(weight * fx, torch.zeros_like(fx))
if __name__ == '__main__':
NumSolsdir = 'NumSols'
Nsample = 80
matfile = NumSolsdir + '/' + 'Burges1D_SampleNum=' + str(Nsample) + '.mat'
M = 2
roeqs = CustomedEqs(matfile, M)
# Net = CustomedNet(roeqs=roeqs,layers=[2,20,20,20,M])
# print(Net.labeledLoss)
from plotting import newfig, savefig
import matplotlib.pyplot as plt
newfig(width=0.8)
plt.semilogy(np.arange(roeqs.sigma.shape[0]) + 1, roeqs.sigma, '-ko')
plt.xlabel('$m$')
plt.ylabel('Singular value')
plt.show()
savefig('fig/SingularValues_%d' % (Nsample))
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Exact $\\varepsilon(t,x)$', fontsize=10)
######## Learned e(t,x,y) ###########
ax = plt.subplot(gs[1:2, 1])
h = plot_solution(t, x, e_pred, ax)
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Learned $\\varepsilon(t,x)$', fontsize=10)
savefig('./figures/turbulence_1D_dissipation', crop=False)
scipy.io.savemat(
'turbulence_1D_dissipation_swish_noise3_results_%s.mat' %
(time.strftime('%d_%m_%Y')), {
't': t,
'x': x,
'u': u,
'e': e,
'u_pred': u_pred,
'e_pred': e_pred
})
ax.set_xlim([-5.1, 5.1])
ax.set_ylim([-0.1, 5.1])
ax = plt.subplot(gs1[0, 1])
ax.plot(x, Exact_h[:, 100], 'b-', linewidth=2, label='Exact')
ax.plot(x, H_pred[100, :], 'r--', linewidth=2, label='Prediction')
ax.set_xlabel('$x$')
ax.set_ylabel('$|h(t,x)|$')
ax.axis('square')
ax.set_xlim([-5.1, 5.1])
ax.set_ylim([-0.1, 5.1])
ax.set_title('$t = %.2f$' % (t[100]), fontsize=10)
ax.legend(loc='upper center',
bbox_to_anchor=(0.5, -0.8),
ncol=5,
frameon=False)
ax = plt.subplot(gs1[0, 2])
ax.plot(x, Exact_h[:, 125], 'b-', linewidth=2, label='Exact')
ax.plot(x, H_pred[125, :], 'r--', linewidth=2, label='Prediction')
ax.set_xlabel('$x$')
ax.set_ylabel('$|h(t,x)|$')
ax.axis('square')
ax.set_xlim([-5.1, 5.1])
ax.set_ylim([-0.1, 5.1])
ax.set_title('$t = %.2f$' % (t[125]), fontsize=10)
savefig('./figures/NLS')
loss_log = np.array(model.loss_log)
np.save('loss/loss_QRes.npy', loss_log)
newfig(width=1)
for k in range(2):
for i in range(alpha.shape[0]):
alphai = alpha[i:i + 1, :]
lamdai = Net(torch.tensor(alphai).float().to(DEVICE))
phi_proj = np.matmul(lamdai, roeqs.Modes.T)
phi_Exact = roeqs.phix(roeqs.xgrid.T, alphai[:, 0:1], alphai[:, 1:2])
#plot
name = '$\\boldsymbol{\\mu}=(%0.1f,%0.1f)$' % (alphai[0, 0], alphai[0,
1])
if k == 0:
plt.plot(roeqs.xgrid,
phi_Exact.T,
colors[i] + lines[0],
label='PS',
markersize=6)
else:
plt.plot(roeqs.xgrid,
phi_proj.T,
colors[i] + symbols[i],
label='PRNN, ' + name,
markersize=6)
plt.xlabel('$x$')
plt.ylabel('$\phi$')
#plt.title(resultsdir)
plt.legend(loc="upper left", ncol=2, handlelength=2, columnspacing=1)
plt.show()
savefig('fig/ResultComparsion')
lambda_1_value, lambda_2_value)
s = s + r' \end{array}$ \\ '
s = s + r' \hline'
s = s + r' Identified PDE (1\% noise) & $\begin{array}{c}'
s = s + r' u_t + %.3f (u u_x + v u_y) = -p_x + %.5f (u_{xx} + u_{yy})' % (
lambda_1_value_noisy, lambda_2_value_noisy)
s = s + r' \\'
s = s + r' v_t + %.3f (u v_x + v v_y) = -p_y + %.5f (v_{xx} + v_{yy})' % (
lambda_1_value_noisy, lambda_2_value_noisy)
s = s + r' \end{array}$ \\ '
s = s + r' \hline'
s = s + r' \end{tabular}$'
ax.text(0.015, 0.0, s)
savefig('./figures/NavierStokes_prediction')
print('Error u: %e' % (error_u))
print('Error v: %e' % (error_v))
print('Error p: %e' % (error_p))
print('Error l1: %.5f%%' % (error_lambda_1))
print('Error l2: %.5f%%' % (error_lambda_2))
print('Error l1: %.5f%%' % (error_lambda_1_noisy))
print('Error l2: %.5f%%' % (error_lambda_2_noisy))
with open('results.txt', 'w') as f:
lines = []
lines.append('Error v: %e\n' % (error_v))
lines.append('Error p: %e\n' % (error_p))
extent=[lb_sol[0], ub_sol[0], lb_sol[1], ub_sol[1]],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Exact Dynamics', fontsize = 10)
line = np.linspace(lb_sol[1], ub_sol[1], 2)[:,None]
ax.plot(t_idn[index]*np.ones((2,1)), line, 'w-', linewidth = 1)
######## Exact p(t,x,y) ###########
ax = plt.subplot(gs[:, 1])
h = ax.imshow(U_pred, interpolation='nearest', cmap='jet',
extent=[lb_sol[0], ub_sol[0], lb_sol[1], ub_sol[1]],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('Learned Dynamics', fontsize = 10)
line = np.linspace(lb_sol[1], ub_sol[1], 2)[:,None]
ax.plot(t_idn[index]*np.ones((2,1)), line, 'w-', linewidth = 1)
savefig('../figures/Burgers')
Y,
zdir='y',
offset=t_star.mean(),
cmap='rainbow',
alpha=0.8)
ax.text(x_star.mean(), data['t'].min() - 1, y_star.min() - 1, '$x$')
ax.text(x_star.max() + 1, data['t'].mean(), y_star.min() - 1, '$t$')
ax.text(x_star.min() - 1, data['t'].min() - 0.5, y_star.mean(), '$y$')
ax.text(x_star.min() - 3, data['t'].mean(), y_star.max() + 1, '$v(t,x,y)$')
ax.set_xlim3d(r1)
ax.set_ylim3d(r2)
ax.set_zlim3d(r3)
axisEqual3D(ax)
savefig('./figures/NavierStokes_data' + str(learning_rate))
fig, ax = newfig(1.015, 0.8)
ax.axis('off')
######## Row 2: Pressure #######################
######## Predicted p(t,x,y) ###########
gs2 = gridspec.GridSpec(1, 2)
gs2.update(top=1, bottom=1 - 1 / 2, left=0.1, right=0.9, wspace=0.5)
ax = plt.subplot(gs2[:, 0])
h = ax.imshow(
PP_star,
interpolation='nearest',
cmap='rainbow',
extent=[x_star.min(),
x_star.max(),
nwalkers = 32
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
log_posterior,
args=(x, y, y_err))
p0 = np.append(w, -5.0)
pos, lp, _ = sampler.run_mcmc(p0 + 1e-4 * np.random.randn(nwalkers, ndim),
5000)
ind = np.argmax(lp)
sampler.reset()
pos, lp, _ = sampler.run_mcmc(
pos[ind] + 1e-4 * np.random.randn(nwalkers, ndim), 5000)
sampler.run_mcmc(pos, 20000)
tau = sampler.get_autocorr_time()
acc_frac = np.mean(sampler.acceptance_fraction)
fig, ax = plt.subplots(1, 1, figsize=SQUARE_FIGSIZE, sharex=True)
ax.errorbar(x, y, yerr=y_err, xerr=x_err, fmt=".k", capsize=0, ms=4)
x0 = np.linspace(0, 10, 3)
samples = sampler.flatchain
for i in np.random.randint(len(samples), size=100):
theta = samples[i]
ax.plot(x0, x0 * theta[0] + theta[1], color="k", alpha=0.05)
ax.plot(x0, 0.5 * x0 - 0.1, label="truth")
ax.plot(x0, np.dot(np.vander(x0, 2), w), label="naive fit")
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.yaxis.set_major_locator(plt.MaxNLocator(4))
plt.legend(fontsize=12, loc=4)
savefig(fig, "line1.pdf")
def plot_pressure(p_pred, p_star, X_star, epoch, learning_rate):
# Predict for plotting
lb = X_star.min(0)
ub = X_star.max(0)
nn = 200
x = np.linspace(lb[0], ub[0], nn)
y = np.linspace(lb[1], ub[1], nn)
X, Y = np.meshgrid(x, y)
PP_star = griddata(X_star,
np.ndarray.flatten(p_pred.numpy()), (X, Y),
method='cubic')
P_exact = griddata(X_star,
np.ndarray.flatten(p_star), (X, Y),
method='cubic')
x_star = X_star[:, 0:1]
y_star = X_star[:, 1:2]
fig, ax = newfig(1.015, 0.8)
ax.axis('off')
######## Predicted p(t,x,y) ###########
gs2 = gridspec.GridSpec(1, 2)
gs2.update(top=1, bottom=1 - 1 / 2, left=0.1, right=0.9, wspace=0.5)
ax = plt.subplot(gs2[:, 0])
h = ax.imshow(
PP_star,
interpolation='nearest',
cmap='rainbow',
extent=[x_star.min(),
x_star.max(),
y_star.min(),
y_star.max()],
origin='lower',
aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
ax.set_aspect('equal', 'box')
ax.set_title('Predicted pressure', fontsize=10)
######## Exact p(t,x,y) ###########
ax = plt.subplot(gs2[:, 1])
h = ax.imshow(
P_exact,
interpolation='nearest',
cmap='rainbow',
extent=[x_star.min(),
x_star.max(),
y_star.min(),
y_star.max()],
origin='lower',
aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
fig.colorbar(h, cax=cax)
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
ax.set_aspect('equal', 'box')
ax.set_title('Exact pressure', fontsize=10)
savefig('./figures/NavierStokes_prediction ' + str(learning_rate) + ' ' +
str(epoch))
plt.close()
pass
# , ticks=[-1, -0.5, 0, 0.5, 1])
# cbar.ax.set_yticklabels(['-1', '-0.5', '0', '0.5', '1'])
cbar.ax.tick_params(labelsize=20)
ax.set_xlim(-0.01, 1)
ax.set_ylim(-1.01, 1.02)
#ax_pred.locator_params(nbins=5)
#ax_pred.set_xticklabels(np.linspace(0,1,5), rotation=0, fontsize=18)
ax.set_xlabel('$t$')
ax.set_ylabel('$x$')
ax.set_title('$ u^{Exact} $')
# for xc in x_interface:
# ax.axhline(y=xc, linewidth=1, color = 'w')
#fig.tight_layout()
fig.set_size_inches(w=15,h=8)
savefig('./figures/BurExact_4sd')#KdV3SD_PredPlot')
# plt.show()
fig, ax = newfig(1.0, 1.1)
# fig = plt.figure()
gridspec.GridSpec(1,1)
ax = plt.subplot2grid((1,1), (0,0))
maxLevel = max(max(u1_star),max(max(u2_star),max(max(u3_star),max(u4_star))))[0]
minLevel = min(min(u1_star),min(min(u2_star), min(min(u3_star), min(u4_star)) ))[0]
levels = np.linspace(minLevel-0.01, maxLevel+0.01, 200)
CS_pred1 = ax.contourf(T1, X1, U1_pred, levels=levels, cmap='jet', origin='lower')
CS_pred2 = ax.contourf(T2, X2, U2_pred, levels=levels, cmap='jet', origin='lower')
CS_pred3 = ax.contourf(T3, X3, U3_pred, levels=levels, cmap='jet', origin='lower')
CS_pred4 = ax.contourf(T4, X4, U4_pred, levels=levels, cmap='jet', origin='lower')
import matplotlib.pyplot as plt
# Run the sampler.
ndim = 2
nwalkers = 32
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_p_func)
sampler.run_mcmc(np.random.randn(nwalkers, ndim), 20000)
tau = sampler.get_autocorr_time()
acc_frac = np.mean(sampler.acceptance_fraction)
with open("numbers-emcee.tex", "w") as f:
f.write("% Automatically generated - emcee\n")
f.write("\\newcommand{{\\eaccfrac}}{{{0:.2f}}}\n".format(acc_frac))
f.write("\\newcommand{{\\etaua}}{{{0:.0f}}}\n".format(tau[0]))
f.write("\\newcommand{{\\etaub}}{{{0:.0f}}}\n".format(tau[1]))
fig, ax = plt.subplots(1, 1, figsize=SQUARE_FIGSIZE, sharex=True)
p = autocorr.function(np.mean(sampler.chain, axis=0))
ax.plot(p[:, 0], label=r"$f(\theta) = \theta_1$")
ax.plot(p[:, 1], label=r"$f(\theta) = \theta_2$")
p = autocorr.function(np.mean(np.prod(sampler.chain, axis=-1), axis=0))
ax.plot(p, label=r"$f(\theta) = \theta_1 \, \theta_2$")
ax.set_title("emcee")
ax.set_ylabel("autocorrelation")
ax.set_xlabel("lag [steps]")
ax.set_xlim(0, 500)
ax.yaxis.set_major_locator(plt.MaxNLocator(4))
ax.xaxis.set_major_locator(plt.MaxNLocator(4))
plt.legend(fontsize=12)
savefig(fig, "ensemble.pdf")
