[petsc-users] Question about using PETSc to generate matrix preconditioners

[Jed Brown]

I think random matrices will produce misleading results. The chance of randomly generating a matrix that resembles an application is effectively zero. I think you'd be better off with some model problems varying parameters that control the physical regime (e.g., shifts to a Laplacian, advection with/without upwinding at varying cell Peclet numbers, varying nondimensional parameters, time step, and boundary layers for fluids, varying Poisson ratio and material contrast in elasticity).

"Sun, Yixuan via petsc-users" <petsc-users at mcs.anl.gov> writes:

> Hello PETSc team,
>
> My name is Yixuan, and I am a postdoc at MCS. We are working on a project where we want to predict the preconditioners from the corresponding matrices. For preliminary exploration purposes, we generated random matrices and their preconditioners using PETSc. The current deep learning models look promising with the generated data. However, we are not sure about the correctness of the data generation code and wanted to ask if you could help check the correctness of our script (< 100 lines) and let us know if there were any issues. Here is the link<https://github.com/iamyixuan/MatrixPreNet/blob/main/src/utils/generate_training.py> to the script.
>
> Please let me know if you have any questions or concerns. Thank you in advance!
>
>
> Warm regards,
> Yixuan
> --------------------
> Yixuan Sun
> Postdoctoral Researcher
> Mathematics and Computer Science
> Argonne National Laboratory