Definition of Helmholtz Equations

[QifengHu]

To whom it may concern,

I am trying to implement the Helmholtz problem in your paper. I tried many times in the basic PINNs, and the prediction is different from the publication, even in the lowest wave number case. After going through your partial code, I found that it might not be consistent with the definition of scalar problem parameters, k and sigma, as well as the source term, in the paper.

Could you please help me clarify the correct definition of the governing equation? The figure 9 is indeed an attractive picture that I want to explore. Thank you very much!

Best,
Qifeng

[benmoseley]

The exact problem class we used for the paper is here:
https://github.com/benmoseley/FBPINNs/blob/multilevel-paper/multilevel-paper/problems.py

Also the exact hyperparameters we used to train the PINNs in the paper are here: https://github.com/benmoseley/FBPINNs/blob/multilevel-paper/multilevel-paper/main.py

This should be all that is needed to reproduce our results