We have an example in src/ts/tutorials/autodiff on using AD for reaction-diffusion equations. It does exactly what Matt said - differentiating the stencil kernel to get the Jacobian kernel. More information is available in this report: https://urldefense.us/v3/__https://arxiv.org/abs/1909.02836__;!!G_uCfscf7eWS!cMXnAlSzQJa8lo5JBEpmUizoHds-gACnH-ecvwbHQpvuta1pc1NbtArflhZa6Td7oV1qIFEndu5eX9P1yjvtqEGquw$
Hong (Mr.) ________________________________ From: petsc-users <petsc-users-boun...@mcs.anl.gov> on behalf of Matthew Knepley <knep...@gmail.com> Sent: Friday, January 17, 2025 6:22 AM To: Zou, Ling <l...@anl.gov> Cc: petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov> Subject: Re: [petsc-users] Auto sparsity detection? On Thu, Jan 16, 2025 at 10:43 PM Zou, Ling <l...@anl.gov<mailto:l...@anl.gov>> wrote: Thank you, Matt. Seems that at least the matrix coloring part I am following the ‘best practice’. Yes, for FD approximations of the Jacobian. If you have a stencil operation (like FEM or FVM), then AD can be very useful because you only have to differentiate the kernel to get the Jacobian kernel. Thanks, Matt -Ling From: Matthew Knepley <knep...@gmail.com<mailto:knep...@gmail.com>> Date: Thursday, January 16, 2025 at 9:01 PM To: Zou, Ling <l...@anl.gov<mailto:l...@anl.gov>> Cc: petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov> <petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>> Subject: Re: [petsc-users] Auto sparsity detection? On Thu, Jan 16, 2025 at 9: 50 PM Zou, Ling via petsc-users <petsc-users@ mcs. anl. gov> wrote: Hi all, Does PETSc has some automatic matrix sparsity detection algorithm available? Something like: https: //docs. sciml. ai/NonlinearSolve/stable/basics/sparsity_detection/ ZjQcmQRYFpfptBannerStart This Message Is From an External Sender This message came from outside your organization. ZjQcmQRYFpfptBannerEnd On Thu, Jan 16, 2025 at 9:50 PM Zou, Ling via petsc-users <petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>> wrote: Hi all, Does PETSc has some automatic matrix sparsity detection algorithm available? Something like: https://urldefense.us/v3/__https://docs.sciml.ai/NonlinearSolve/stable/basics/sparsity_detection/__;!!G_uCfscf7eWS!cMXnAlSzQJa8lo5JBEpmUizoHds-gACnH-ecvwbHQpvuta1pc1NbtArflhZa6Td7oV1qIFEndu5eX9P1yjs2FwvpFg$ <https://urldefense.us/v3/__https:/docs.sciml.ai/NonlinearSolve/stable/basics/sparsity_detection/__;!!G_uCfscf7eWS!ccEx6zmuNrVADqtN50hO2N0k4Qs-A70nztAjMLu-JElnjhK5w84BpYC8CAINd6KihSxaS2rx_LgpqUVM49U$> Sparsity detection would rely on introspection of the user code for ComputeFunction(), which is not possible in C (unless you were to code up your evaluation in some symbolic framework). The background is that I use finite differencing plus matrix coloring to (efficiently) get the Jacobian. For the matrix coloring part, I color the matrix based on mesh connectivity and variable dependencies, which is not bad, but just try to be lazy to even eliminating this part. This is how the automatic frameworks also work. This is how we compute the sparsity pattern for PetscFE and PetscFV. A related but different question, how much does PETSc support automatic differentiation? I see some old paper: https://ftp.mcs.anl.gov/pub/tech_reports/reports/P922.pdf and discussion in the roadmap: https://urldefense.us/v3/__https://petsc.org/release/community/roadmap/__;!!G_uCfscf7eWS!cMXnAlSzQJa8lo5JBEpmUizoHds-gACnH-ecvwbHQpvuta1pc1NbtArflhZa6Td7oV1qIFEndu5eX9P1yjtgW1TJuw$ <https://urldefense.us/v3/__https:/petsc.org/release/community/roadmap/__;!!G_uCfscf7eWS!ccEx6zmuNrVADqtN50hO2N0k4Qs-A70nztAjMLu-JElnjhK5w84BpYC8CAINd6KihSxaS2rx_Lgpw6v6hKE$> I am thinking that if AD works so I don’t even need to do finite differencing Jacobian, or have it as another option. Other people understand that better than I do. Thanks, Matt Best, -Ling -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cMXnAlSzQJa8lo5JBEpmUizoHds-gACnH-ecvwbHQpvuta1pc1NbtArflhZa6Td7oV1qIFEndu5eX9P1yjtIbKZadg$ <https://urldefense.us/v3/__http:/www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!d-7O5V0pNvm_fDSKhNk_ilXP0jG-_MBnectBJ0BfVPOSzARXvYWAahGyRNf1cKCh9dJKEiFt2caV$> -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cMXnAlSzQJa8lo5JBEpmUizoHds-gACnH-ecvwbHQpvuta1pc1NbtArflhZa6Td7oV1qIFEndu5eX9P1yjtIbKZadg$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cWyHnKq-Gzasz3ooIUAgTl0RTGrzg0fW8jwVOi0AHE_Ydv4dnayXiG06EPQYvp6guWhXYTv8DMnOu7xNNzJR$>
