STMsFNN performs poorly on the 2D wave equation
#492
Comments
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The initial loss is 1.03e+16, so it seems the scaling has an issue. |
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Thank you for the suggestions, @lululxvi! I made some changes to my code and now it seems to do a bit better. But I still am not able to get the desired output -
import numpy as np
import pandas as pd
import deepxde as dde
from deepxde.backend import tf
import matplotlib.pyplot as plt
c = 10 # wave equation constant
C = 1 # Fourier constant
n = 1
m = 1
# dimensions
a = 1
b = 1
def pde(x, u):
u_tt = dde.grad.hessian(u, x, i=2, j=2)
u_xx = dde.grad.hessian(u, x, i=0, j=0)
u_yy = dde.grad.hessian(u, x, i=1, j=1)
return u_tt - ((c ** 2) * (u_xx + u_yy))
def sol(x):
return (
C
* np.sin(m * np.pi * x[:, 0:1] / a)
* np.sin(n * np.pi * x[:, 1:2] / b)
* np.cos(np.sqrt(2) * np.pi * c * x[:, 2:3]) # (m^2/a^2 + n^2/b^2) = 2
)
def boundary_init(x, _):
return np.isclose(x[-1], 0)
def get_initial_loss(model):
model.compile("adam", lr=0.001, metrics=["l2 relative error"])
losshistory, _ = model.train(0)
return losshistory.loss_train[0]
spatial_domain = dde.geometry.Rectangle(xmin=[0, 0], xmax=[a, b])
temporal_domain = dde.geometry.TimeDomain(0, 1)
spatio_temporal_domain = dde.geometry.GeometryXTime(spatial_domain, temporal_domain)
d_bc = dde.DirichletBC(
spatio_temporal_domain, lambda x: 0, lambda _, on_boundary: on_boundary
)
ic = dde.IC(
spatio_temporal_domain,
lambda x: np.sin(np.pi * x[:, 0:1]) * np.sin(np.pi * x[:, 1:2]),
lambda _, on_initial: on_initial,
)
ic_2 = dde.OperatorBC(
spatio_temporal_domain,
lambda x, u, _: dde.grad.jacobian(u, x, i=0, j=1),
boundary_init,
)
data = dde.data.TimePDE(
spatio_temporal_domain,
pde,
[d_bc, ic, ic_2],
num_domain=360,
num_boundary=360,
num_initial=360,
num_test=10000,
solution=sol,
)
net = dde.nn.STMsFFN(
[3] + [100] * 3
# + [300] * 2 + [100] * 2
+ [1],
"tanh",
"Glorot uniform",
# sigmas_x=[100, 250, 500, 1000, 1250],
# sigmas_t=[100, 250, 500, 1000, 1250, 1500, 2500],
sigmas_x=[100, 150, 200, 250, 500,],
sigmas_t=[100, 150, 200, 250, 500, 750, 1000],
)
net.apply_feature_transform(lambda x: x / 250)
model = dde.Model(data, net)
initial_losses = get_initial_loss(model)
loss_weights = 1 / (2 * initial_losses)
model.compile(
"adam",
lr=0.001,
metrics=["l2 relative error"],
# decay=("inverse time", 5000, 0.9),
decay=("inverse time", 10000, 0.9),
loss_weights=loss_weights,
)
pde_residual_resampler = dde.callbacks.PDEResidualResampler(period=1)
losshistory, train_state = model.train(epochs=20000, callbacks=[pde_residual_resampler], display_every=500)
dde.saveplot(
losshistory,
train_state,
issave=True,
isplot=True,
test_fname="../dat_data/wave_2D.dat",
) |
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The loss seems still large. You have only trained for 20000 steps. Have you tried the similar PDE but for a simpler solution (smoother)? |
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Is it possible to use STMsFFN without an exact solution? |
Yes, the same usage as other networks. |
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@Saransh-cpp Hey, just wanted to add here. Incase any else faces this issue! It should be I was using operatorBC as used above, and spent almost 2 days and 100 experiments, to get stupid results. Since, this is a 2D case, your input vector would be [X,Y,T]. |
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Greetings,
I have been trying to use the
Spatio Temporal Multi-scale Fourier feature networkson the 2-dimensional wave equation, but the network performs poorly and is not able to pick up high-frequency details.Plots
Losses and metric
Plot 1 (y, u, and t)
Plot 2 (x, u, and t)
Code
Output
I have tried varying every hyperparameter but I can't get the network to learn the solution accurately. Could someone please help me with this?
Thank you!
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