Differentiabiliity Comparison for various AD backends.

[KapilKhanal]

@mancellin Differentiability comparison.

using MarineHydro
using Enzyme 
using ReverseDiff
using StaticArrays
using BenchmarkTools
using Zygote
using ForwardDiff

wavenumber = 1.0

println("WITH STATIC VECTORS")

element_1 = (
    center=SVector(0.0, 0.0, -1.0), 
)

element_2 = (
    center=SVector(1.0, 1.0, -2.0),
    vertices=@SMatrix([-0.5 -0.5 0.0; 
                        0.5 -0.5 0.0; 
                        0.5  0.5 0.0; 
                       -0.5  0.5 0.0]) .+ SVector(1.0, 1.0, -2.0)',
    normal=SVector(0.0, 0.0, 1.0),
    radius=sqrt(2)/2,
    area=1.0,
)

println("Rankine")

function S(z::Float64)::Float64
    center = SVector(0.0, 0.0, z)
    MarineHydro.integral(Rankine(), (center=center,), element_2)
end

function D(z::Float64)::Vector{Float64}
    center = SVector(0.0, 0.0, z)
    result =  MarineHydro.integral_gradient(Rankine(), (center=center,), element_2)
    Vector{Float64}(result)
end


println("Benchmarking Enzyme.gradient:")
@btime Enzyme.gradient(Forward, S, 1.0)


println("Benchmarking Enzyme.jacobian:")
@btime Enzyme.jacobian(Reverse, D, -1.0)


println(" ForwardDiff")
x = -1.0
@btime ForwardDiff.derivative(S, x)
@btime ForwardDiff.derivative(D, x)

println(" GFWu")
S(z) = real(MarineHydro.integral(GFWu(), (center=[0.0, 0.0, z],), element_2, wavenumber))
D(z) = real.(MarineHydro.integral_gradient(GFWu(), (center=[0.0, 0.0, z],), element_2, wavenumber))

println(" Zygote")
@btime Zygote.gradient($S, $(-1.0))
@btime Zygote.jacobian($D, $(-1.0))


println(" ForwardDiff")
x = -1.0
@btime ForwardDiff.derivative(S, x)
@btime ForwardDiff.derivative(D, x)

println(" Enzyme")
@btime Enzyme.gradient(Forward, S, x)
@btime Enzyme.jacobian(Reverse,D, x)

Output:

WITH STATIC VECTORS
Rankine
Benchmarking Enzyme.gradient:
  508.435 ns (5 allocations: 128 bytes)
Benchmarking Enzyme.jacobian:
  8.986 μs (77 allocations: 4.50 KiB)
 ForwardDiff
  400.139 ns (5 allocations: 224 bytes)
  859.802 ns (9 allocations: 928 bytes)
 GFWu
 Zygote
  844.508 μs (2601 allocations: 88.83 KiB)
  6.797 ms (14627 allocations: 485.34 KiB)
 ForwardDiff
  385.881 ns (5 allocations: 224 bytes)
  866.700 ns (9 allocations: 928 bytes)
 Enzyme
  536.180 ns (6 allocations: 144 bytes)
  9.431 μs (78 allocations: 4.52 KiB)

[mancellin]

I discovered this package recently that might help with this kind of benchmark: https://juliadiff.org/DifferentiationInterface.jl/DifferentiationInterfaceTest/stable/

[mancellin]

Does Enzyme works on a full SVector function?