Trying to find the correct weights for BCs, seems not working

[mercury-4600]

Hi Dr. Lu,

First, Thanks for your amazing contribution.

I would like to use DeepXDE to solve a Laplace equation on a disk, I have settled all of it's boundary conditions(it gots 3 BCs in codes) and used specific training points, it can work normally without any report errors, but still failed to get the correct solution. And so far, I have tried some methods in the issue to reduce my error, like :

• Used more specific training points and added more on BCs;
• Used larger network structure;
  And I tried adding weights as you have mentioned in
  1D simple transient diffusion PDE with 2 Neumann BCs  #40
  The weights I added is :

model.compile("adam", lr=1e-3, metrics=["l2 relative error"],loss_weights=[3,1.3e-1,1.3e-1,1.3e-1,1.3e-1,7.8e-2,7.8e-2])
The solution is still unsatisfactory, I thought its because I didn't set a correct distribution of weights for each item, so I added a simple traversal search method to help me find the suitable distributions:

The simple search method I added is a nested for loop：
for w1 in range(10, 100, 10):
for w2 in range(10, 100, 10):
for w3 in range(10, 100, 10):
model.compile("adam", lr=1e-3, metrics=["l2 relative error"], loss_weights=[w, w2,w2,w2,w2,w3,w3])
losshistory, train_state = model.train(epochs= 5000)
if error_max <= s:
print("Error ends at:",error_max)
print("W ends at:",w1, w2 , w2 , w2 , w2, w3 , w3 )
The s is a ideal difference from the correct solution. After few day's trying, it seems not working, because the error I got at each epoch is similar, or saying that the change steps of w1,w2,w3 have imperceptible effect on error.

So I wonder:

1. If this way is feasible or not, could I find a suitable weights for the BCs in order to get the correct solution?
2. What else I can do to find the correct solution?

[lululxvi]

Here is the code of Laplace equation on a disk: https://deepxde.readthedocs.io/en/latest/demos/pinn_forward/laplace.disk.html