Mistake in computing derivatives of u

[KemasZakaria]

in this code snippet, you are computing the derivatives of sum(u) instead of the derivatives of u

u = net(x,t)   

u_x = torch.autograd.grad(u.sum(), x, create_graph=True)[0]

u_t = torch.autograd.grad(u.sum(), t, create_graph=True)[0]

pde = u_x - 2*u_t - u

return pde

This means that the PINN doesn't exactly satisfy the PDE, but rather changing the term du/dx into d(sum_u)/dx in the differential equation. While this may work on some cases (typically simple case with no near discontinuity), the code won't be able to solve more complex problems. Even problems such as Burgers' equation with small viscosity (which is considered as simple problems, shown in the paper that you cite) can't be solved with this PINN . So I suggest to change the code into

u_x = torch.autograd.grad(u, x, grad_outputs = torch.ones_like(u), retain_graph = True, create_graph=True)[0]

u_t = torch.autograd.grad(u, t, grad_outputs = torch.ones_like(u), retain_graph = True, create_graph=True)[0]

pde = u_x - 2*u_t - u

return pde

this will correctly compute the derivatives of u instead of sum(u)