Better results with Periodic boundary conditions

[camolina2]

Dear Lulu,

I would like to ask you if you have any idea of this results.

I have exactly the same problem to solve and in the boundary conditions I have better results when I define my conditons as Periodic boundary conditions than with the Exact solution.

Do you have any idea why this could happend?

Thank you in advance

[lululxvi]

No idea.

[camolina2]

Could you please give me the sense or idea of the information that is been given in the loss function with the periodic boundary conditions ?

I understand that the network is making prediction in the border with the periodic boundary conditions and in the loss function is the difference between them. Is it this correct?

Thank you so much in advance

[athtareq]

Could you please give me the sense or idea of the information that is been given in the loss function with the periodic boundary conditions ?

I understand that the network is making prediction in the border with the periodic boundary conditions and in the loss function is the difference between them. Is it this correct?

Thank you so much in advance

I think the loss is the norm of the difference between the real PDE & BC applied to random points and the prediction of the network applied to the same random points. It's in the article https://epubs.siam.org/doi/10.1137/19M1274067

[camolina2]

@athtareq Yes! I think the same! Thank you so much!