search

lululxvi / deepxde

A library for scientific machine learning and physics-informed learning
https://deepxde.readthedocs.io
GNU Lesser General Public License v2.1
2.71k stars 753 forks source link

Better results with Periodic boundary conditions #879

Open camolina2 opened 2 years ago

camolina2 commented 2 years ago

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 commented 2 years ago

No idea.

camolina2 commented 2 years ago

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 commented 2 years ago

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 commented 2 years ago

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