AD Section in Documentation

[avik-pal]

TODOs

• Merge What is a Nonlinear Solver? And How to easily build Newer Ones #345
• Finish Add PolyesterForwardDiff Support JuliaDiff/SparseDiffTools.jl#281
• Add a section on AD tips in the documentation

Good Old Brusselator Benchmark

julia> @btime solve(prob_brusselator_2d, NewtonRaphson());
  402.717 ms (6959 allocations: 64.87 MiB)

julia> using PolyesterForwardDiff

julia> @btime solve(prob_brusselator_2d, NewtonRaphson());
  348.450 ms (333 allocations: 77.20 MiB)

Not changing the default, here, but mentioned in the docs on how to use polyester.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (7e0685a) 86.19% compared to head (812f6fb) 75.81%.
Report is 11 commits behind head on master.

Additional details and impacted files

@@             Coverage Diff             @@
##           master     #354       +/-   ##
===========================================
- Coverage   86.19%   75.81%   -10.39%     
===========================================
  Files          44       44               
  Lines        2608     2605        -3     
===========================================
- Hits         2248     1975      -273     
- Misses        360      630      +270     

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[avik-pal]

I want to verify that this is better in most cases before switching the default

[avik-pal]

@oscardssmith do you know what https://github.com/SciML/NonlinearSolve.jl/actions/runs/7786112451/job/21230175067?pr=354#step:6:14951 is? It seems to come from the Base.Experimental.@opaque, which I think you added.

[oscardssmith]

It is. It means you are trying to AD a function even though the test specifically tells you not to AD it.