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Question

Thx a lot for the repo first of all.

My question would be about the Helmholtz problem (https://github.com/cmgcds/fastvpinns/blob/main/examples/forward_problems_2d/complex_mesh/helmholtz2d/main_helmholtz.py)

Helmholtz problem has two components of the residual loss; x and y contributions, requiring two components of Jacobian (J_x and J_y) as Kharizmi's implementation as well. However, you don't introduce the components of Jacobian. Or do I miss a point?

First of all, I sincerely apologize for my late reviews. I encountered some unforeseeable issues recently, which delayed my response to your manuscript. Thank you again for understanding.

Overall, it is an awesome software package dedicated to hp-VPINNs. The statement of need is clear and well-motivated to me. The tutorials are helpful and the API documents are thorough.

The only concerns I have are:

1. #16 I believe the tutorial docs should be fixed this way but correct me if wrong
2. One of the claims in the manuscript is that this package can read external mesh from a .mesh file. This is substantiated in the tutorial scripts as they indeed load mesh from a .mesh file. However, it is not so clear how a .mesh file is generated from GMSH package. I suggest a short tutorial script on how to generate a .mesh file from a user-defined mesh, especially one that is slightly more "complicated" or "arbitrary" than uniform mesh or circular mesh. With this tutorial, one could examine the applicability of this package to more realistic problems at hand where the mesh is somehow irregular.

Dear all,
I successfully installed the library from the DeepXde Docker image, which includes TensorFlow 2.9.2.

For your information, I had to further install the following libraries:

apt-get install libgl1-mesa-glx
apt-get install libglu1
apt-get install libxcursor-dev
apt-get install libxft2
apt-get install libxinerama

Is it a known behavior?

It could be beneficial to build a dedicated image for fastvpinns, for reproducibility purposes.
I could help you with this.

Finally, do you recommend any version of TensorFlow?
Best,