pinnsformer's Issues
The derivative in the code
I have been closely examining the implementation of the Navier-Stokes equation in your code and I appreciate the effort put into this work. I have a query regarding the computation of the second-order derivative, specifically u_xx
.
In the code, the second-order derivative u_xx
is calculated directly from u
with respect to x_train
, as shown below:
u_xx = torch.autograd.grad(u, x_train, ...)
However, I believe that to obtain the second-order derivative u_xx
, we should first compute the first-order derivative u_x
with respect to x_train
, and then differentiate u_x
with respect to x_train
again, like this:
u_x = torch.autograd.grad(u, x_train, ..., create_graph=True)[0]
u_xx = torch.autograd.grad(u_x, x_train, ...)[0]
Could you please confirm if my understanding is correct? If so, would it be possible to update the code accordingly to reflect this change?
Thank you for your time and consideration. I look forward to your response.
Some confusions in `1d_wave_pinn_ntk`
Hello, great work!
According to the NTK algorithm for PINNs in When and why PINNs fail to train: A neural tangent kernel perspective
, I am quite puzzled by the process of solving for J1-J3
below.
Based on my understanding, J1
should be the Jacobian matrix of J2
should be the Jacobian matrix of J3
?
...
...
for i in tqdm(range(1000)):
if i % 50 == 0:
J1 = torch.zeros((D1, n_params))
J2 = torch.zeros((D2, n_params))
J3 = torch.zeros((D3, n_params))
batch_ind = np.random.choice(len(x_res), kernel_size, replace=False)
x_train, t_train = x_res[batch_ind], t_res[batch_ind]
pred_res = model(x_train, t_train)
pred_left = model(x_left, t_left)
pred_upper = model(x_upper, t_upper)
pred_lower = model(x_lower, t_lower)
for j in range(len(x_train)):
model.zero_grad()
pred_res[j].backward(retain_graph=True)
J1[j, :] = torch.cat([p.grad.view(-1) for p in model.parameters()])
for j in range(len(x_left)):
model.zero_grad()
pred_left[j].backward(retain_graph=True)
J2[j, :] = torch.cat([p.grad.view(-1) for p in model.parameters()])
for j in range(len(x_lower)):
model.zero_grad()
pred_lower[j].backward(retain_graph=True)
pred_upper[j].backward(retain_graph=True)
J3[j, :] = torch.cat([p.grad.view(-1) for p in model.parameters()])
...
...
Here is the code I have roughly modified, I am not sure if it is correct.
J1 = torch.zeros((D1, n_params))
J2 = torch.zeros((D2, n_params))
J3 = torch.zeros((D3, n_params))
batch_ind = np.random.choice(len(x_res), kernel_size, replace=False)
x_train, t_train = x_res[batch_ind], t_res[batch_ind]
pred_res = model(x_train, t_train)
pred_left = model(x_left, t_left)
pred_upper = model(x_upper, t_upper)
pred_lower = model(x_lower, t_lower)
u_x = torch.autograd.grad(pred_res, x_train, grad_outputs=torch.ones_like(pred_res), retain_graph=True, create_graph=True)[0]
u_xx = torch.autograd.grad(u_x, x_train, grad_outputs=torch.ones_like(pred_res), retain_graph=True, create_graph=True)[0]
u_t = torch.autograd.grad(pred_res, t_train, grad_outputs=torch.ones_like(pred_res), retain_graph=True, create_graph=True)[0]
u_tt = torch.autograd.grad(u_t, t_train, grad_outputs=torch.ones_like(pred_res), retain_graph=True, create_graph=True)[0]
wave_opt = u_tt - 4 * u_xx # wave operator
del u_x, u_xx, u_t, u_tt
pred_t = torch.autograd.grad(pred_left, t_left, grad_outputs=torch.ones_like(pred_left), retain_graph=True, create_graph=True)[0]
for j in range(len(x_train)):
model.zero_grad()
wave_opt[j].backward(retain_graph=True)
J1[j, :] = torch.cat([p.grad.view(-1) if p.grad is not None else torch.tensor([0.]).view(-1) for p in model.parameters()])
for j in range(len(x_left)):
model.zero_grad()
pred_t[j].backward(retain_graph=True)
J2[j, :] = torch.cat([p.grad.view(-1) if p.grad is not None else torch.tensor([0.]).view(-1) for p in model.parameters()])
for j in range(len(x_lower)):
model.zero_grad()
pred_left[j].backward(retain_graph=True)
pred_lower[j].backward(retain_graph=True)
pred_upper[j].backward(retain_graph=True)
J3[j, :] = torch.cat([p.grad.view(-1) for p in model.parameters()])
How to add dimension to my input
代码中默认的输入是(x,t),但是我希望输入是(x,y,t)。我应该如何做
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