Differentiability tests for time stepping

[maximilian-gelbrecht]

Work in progress

While doing so I restructered all the differentiability tests und put them in a separate folder.

[maximilian-gelbrecht]

I found the issue regarding RingGrids 🎉

We were apperently missing definitions of Base.dataids in our RingGrids that help unalias mutable variables within structs. The docstring of that function does actually recommend that array wrapper structs do implement it, but it's not part of the public API.

[maximilian-gelbrecht]

Some problems with our code with Enzyme in Julia 1.11 that work in Julia 1.10 (see e.g. the CI report), a minimal example without SpeedyWeather posted there EnzymeAD/Enzyme.jl#2295

[maximilian-gelbrecht]

I was able to fix the correctness tests for the high-level timestepping! tests now quite quickly. So it seems we can in fact differentiate through all models correctly!

There's still something wrong for the more detailed tests of the primitive equation model, but I assume that's just user error, as the more high-level tests are correct.

There's not so much remaining to do here. Enzyme in Julia 1.11 is a bit of an issue, but also partially outside of our control.

@milankl I am off work for a week, I think this is already a good time for a proper code review in the meanwhile

[maximilian-gelbrecht]

Adding Enzyme to the docs and actually running the example code, makes the whole CI process for the docs much longer. So long actually, the process timed out. We may also just hardcode the Enzyme example in the docs.

[milankl]

Happy with that for now! We can later check how to automate tests if that's currently unfeasible

[maximilian-gelbrecht]

As an outlook: I did already try to differentiate through multiple time steps with run! as well. And this does seem to work (correctness not separately checked), but of course for any actually longer runs, naively differentiating through everything becomes unfeasible due to the memory usage. This is when one needs to think about checkpointing e.g. with Checkpointing.jl.

[maximilian-gelbrecht]

I actually skip the test in the regular CI for Julia 1.11. I think that's fine for now. I'd rather merge this sooner than later, and continue work on differentiability in further PRs.