Geoscience examples for discrete adjoints and reverse AD

[ToshiyukiBandai]

Hi,

First, congratulations on the excellent review on the exciting topic! I would like to introduce my paper as a geoscience example for discrete adjoints and reverse AD.

In our latest research, we developed a fully-differentiable solver for a nonlinear time-dependent PDE on JAX, and estimate the constitutive relations via neural networks embedded in the PDE. Rather than implementing discrete adjoint methods, we implemented implicit differentiation as a custom derivative rule for the nonlinear solver (probably equivalent to Jilia's way mentioned at the end of section 3.9.2?).
Aside from the paper, in Chapter 4 of my PhD thesis, I compared discrete and continuous adjoint methods for the same PDE.

Hope they are helpful!