Switch from AbstractDifferentiation to DifferentiationInterface

[gdalle]

Following our discussion per email, this PR proposes a switch from AbstractDifferentiation.jl to DifferentiationInterface.jl, which is becoming the new standard in the ecosystem.

• Modify Project.toml files and imports
• Replace SomethingBackend() with AutoSomething()
• Replace value_and_gradient_closure with value_and_gradient (unclear how performance is affected)
• Update documentation and README
• Add preparation mechanism: available on another branch but not sure we want it because if the function contains value-dependent control flow, preparation is not appropriate

[gdalle]

Any idea why the benchmarks fail? Or opinions on the preparation mechanism, which I could add to the present PR?

[lostella]

@gdalle thanks for this! I need to take a deeper look into why the benchmarks fail, seems like something ends up in an endless loop, so maybe it's something to fix upstream.

Regarding preparation: maybe it can be added separately, with some mechanism to make it optional

[lostella]

@gdalle #94 fixed the benchmark, apologies for the conflicts

[gdalle]

Fixed the conflicts, this should be good to go! We can always discuss preparation in a separate PR

[gdalle]

@lostella can you authorize the workflows?

[gdalle]

It seems the benchmarks worked for the PR branch but failed for the main branch?

[lostella]

Yes I think this is expected, since the change is breaking and the benchmark code won't work with the previous commit, right? I don't know of a better method to organize benchmarks for these cases.

I think it's fine, nothing to worry about. I'll just take a manual look at performance before merging, otherwise this looks good, thank you!

[gdalle]

Hi @lostella, just popping by to see if you need anything else from me