Use HyperHessians instead of ForwardDiff to compute the hessian in the Landau example

[KristofferC]

I dusted off my four-year-old https://github.com/KristofferC/HyperHessians.jl, and it seems to still be quite good. Benchmarks run on 1.10 due to JuliaLang/julia#60241 and JuliaLang/julia#60243.

The package has had very little real world use but seems to work here at least and be quite a bit better.

# Fdiff
Single: 11.576176 seconds (1.00 M allocations: 2.434 GiB, 2.04% gc time)
Multi:   5.107421 seconds (994.12 k allocations: 2.397 GiB, 0.85% gc time)
Time for ∇²F! in multi: 0.195347 seconds (92.65 k allocations: 46.968 MiB)


# HyperHessians
Single:  8.298370 seconds (10.95 k allocations: 1.731 GiB, 2.51% gc time)
Multi:    3.529221 seconds (88.96 k allocations: 1.739 GiB, 0.37% gc time)
Time for ∇²F! in multi: 0.114557 seconds (2.65 k allocations: 282.797 KiB)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.19%. Comparing base (65773c2) to head (6ad922e).

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1253   +/-   ##
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  Coverage   94.19%   94.19%           
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  Files          40       40           
  Lines        6662     6662           
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  Hits         6275     6275           
  Misses        387      387           

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[termi-official]

After some discussion on slack I think I am convinced for now that the typical user won't find a way to trigger perturbation confusion when sticking to this example.

[KristofferC]

Maybe I'll register the package and see if some people have an interest in poking on it before mergin thits.

I would also like to get a reverse AD backend working on this to see what effect it has on performance. I started a DifferentiationInterface rewrite (17edffa#diff-bd098a9030f95d6512cf21c19a06a92acd264a6ca5b80f683ca379a0832abec5) but I got into troubles with every reverse AD backend I tried...

[gdalle]

Let me know if I can help with DI integration!

[KristofferC]

The DI integration works fine and was very easy (great job) . It's just that no backend work... 😅

[gdalle]

If you have Mooncake issues, don't hesitate to open them on the repo! It's a small team but they do their best!

[KristofferC]

Ok, opened chalk-lab/Mooncake.jl#867.

[gdalle]

Thanks! What kind of error do you get with Enzyme?

[KristofferC]

Testing backend: Enzyme
┌ Error: Backend Enzyme failed
│   exception =
│    TaskFailedException
│    
│        nested task error: AssertionError: ety == eltype(vt)
│        Stacktrace:
│          [1] sret_ty(fn::LLVM.Function, idx::Int64)
│            @ Enzyme ~/.julia/packages/Enzyme/OhLFb/src/utils.jl:556
│          [2] removeDeadArgs!(mod::LLVM.Module, tm::LLVM.TargetMachine, post_gc_fixup::Bool)
│            @ Enzyme.Compiler ~/.julia/packages/Enzyme/OhLFb/src/llvm/transforms.jl:2476
│          [3] optimize!(mod::LLVM.Module, tm::LLVM.TargetMachine)
│            @ Enzyme.Compiler ~/.julia/packages/Enzyme/OhLFb/src/compiler/optimize.jl:191
│          [4] compile_unhooked(output::Symbol, job::GPUCompiler.CompilerJob{Enzyme.Compiler.EnzymeTarget{GPUCompiler.NativeCompilerTarget}, Enzyme.Compiler.EnzymeCompilerParams{Enzyme.Compiler.PrimalCompilerParams}})
│            @ Enzyme.Compiler ~/.julia/packages/En

EnzymeAD/Enzyme.jl#2794 might be a smaller MWE.

[wsmoses]

just for fun what if you use Enzyme from within reactant (the sret stuff above doesn't matter there)

[KristofferC]

I don't know what that means :)