Laplace equation over a 2D square domain with a hole

[wonghiram]

I am training a Laplace equation with PINN. The solution area and boundary conditions of my research are shown in the figure below.

Below is part of my code.
outer_geom = dde.geometry.Rectangle([0, 0], [1, 1]) inner_geom = dde.geometry.Rectangle([0.4, 0.4], [0.6, 0.6]) def boundary_outer(x, on_boundary): return on_boundary and outer_geom.on_boundary(x) def boundary_inner(x, on_boundary): return on_boundary and inner_geom.on_boundary(x) geom = outer_geom - inner_geom bc_inner = dde.icbc.DirichletBC(geom, lambda x: 1, boundary_inner) bc_outer = dde.icbc.DirichletBC(geom, lambda x: 0, boundary_outer) bc = [bc_inner, bc_outer] data = dde.data.PDE(geom, pde_laplace, bc, num_domain=1500, num_boundary=1520, num_test=2500) net = dde.nn.FNN([2] + [30] * 10 + [1], "tanh", "Glorot uniform") model = dde.Model(data, net) loss_weights = [1, 100, 10] model.compile("adam", lr=0.001, loss_weights=loss_weights) model.train(epochs=50000) model.compile("L-BFGS") losshistory, train_state = model.train()
But the training results are weird. As shown below, the interior boundary does not satisfy the Dirichlet boundary condition U=1.

What is causing this problem and how can I improve the code?

[lululxvi]

Your code is hard to read.

[wonghiram]

Sorry.
Here is a screenshot of my code.
Can you give me some suggestions?

[lululxvi]

Try a larger weight for the inner BC loss.