PDE solution accuracy on differently shaped domains

[marijanarra]

Hi Lu Lu,

I want to solve a Laplace equation on different polygonal domains with Neumann BCs dependent on lengths of the edges and surfaces of the corresponding polygons.

I know that PINNs are scale dependent so I'm concerned about the difference in accuracy of the solutions I would be getting for differently shaped polygons. On the pics below I plotted the error distribution (colorcoded) for the each polygon for 20x2 NN and converged losses. I cannot make sense of the error distributions. Do you maybe have some thoughts on how to approach these kind of domain-scale sensitive problems?

Thanks in advance for your input!

[lululxvi]

Unfortunately, I don't have experience with this.