Diffusion operator loop sparse AD benchmarks

using DifferentiationInterface
using DifferentiationInterfaceTest
using Chairmarks
using DataFrames
using LinearAlgebra
using SparseConnectivityTracer: TracerSparsityDetector
using SparseMatrixColorings
import Chairmarks
import Enzyme, ForwardDiff, Mooncake
import Markdown, PrettyTables, Printf

Backends tested

bcks = [
    AutoEnzyme(mode = Enzyme.Reverse),
    AutoEnzyme(mode = Enzyme.Forward),
    AutoMooncake(config = nothing),
    AutoForwardDiff(),
    AutoSparse(
        AutoForwardDiff();
        sparsity_detector = TracerSparsityDetector(),
        coloring_algorithm = GreedyColoringAlgorithm()
    ),
    AutoSparse(
        AutoEnzyme(mode = Enzyme.Forward);
        sparsity_detector = TracerSparsityDetector(),
        coloring_algorithm = GreedyColoringAlgorithm()
    )
]

6-element Vector{ADTypes.AbstractADType}:
 ADTypes.AutoEnzyme(mode=EnzymeCore.ReverseMode{false, false, false, Enzyme
Core.FFIABI, false, false}())
 ADTypes.AutoEnzyme(mode=EnzymeCore.ForwardMode{false, EnzymeCore.FFIABI, f
alse, false, false}())
 ADTypes.AutoMooncake()
 ADTypes.AutoForwardDiff()
 ADTypes.AutoSparse(dense_ad=ADTypes.AutoForwardDiff(), sparsity_detector=S
parseConnectivityTracer.TracerSparsityDetector(), coloring_algorithm=Sparse
MatrixColorings.GreedyColoringAlgorithm{:direct, 1, Tuple{SparseMatrixColor
ings.NaturalOrder}}((SparseMatrixColorings.NaturalOrder(),), false))
 ADTypes.AutoSparse(dense_ad=ADTypes.AutoEnzyme(mode=EnzymeCore.ForwardMode
{false, EnzymeCore.FFIABI, false, false, false}()), sparsity_detector=Spars
eConnectivityTracer.TracerSparsityDetector(), coloring_algorithm=SparseMatr
ixColorings.GreedyColoringAlgorithm{:direct, 1, Tuple{SparseMatrixColorings
.NaturalOrder}}((SparseMatrixColorings.NaturalOrder(),), false))

Diffusion operator simple loop

uin() = 0.0
uout() = 0.0
function Diffusion(u)
    du = zero(u)
    for i in eachindex(du, u)
        if i == 1
            ug = uin()
            ud = u[i + 1]
        elseif i == length(u)
            ug = u[i - 1]
            ud = uout()
        else
            ug = u[i - 1]
            ud = u[i + 1]
        end
        du[i] = ug + ud - 2*u[i]
    end
    return du
end;

Manual jacobian

function DDiffusion(u)
    A = diagm(
        -1 => ones(length(u)-1),
        0=>-2 .* ones(length(u)),
        1 => ones(length(u)-1))
    return A
end;

Define Scenarios

u = rand(1000)
scenarios = [Scenario{:jacobian, :out}(Diffusion, u; res1 = DDiffusion(u))];

Run Benchmarks

df = DataFrame(benchmark_differentiation(bcks, scenarios))
table = PrettyTables.pretty_table(
    String,
    df;
    backend = :markdown,
    column_labels = names(df),
    formatters = [PrettyTables.fmt__printf("%.1e")]
)

Markdown.parse(table)

Test Summary:                                                              
                                                                           
                                                                           
                                                                           
                                                                  | Pass  T
otal     Time
Testing benchmarks                                                         
                                                                           
                                                                           
                                                                           
                                                                  |   12   
  12  3m17.2s
  ADTypes.AutoEnzyme(mode=EnzymeCore.ReverseMode{false, false, false, Enzym
eCore.FFIABI, false, false}())                                             
                                                                           
                                                                           
                                                                  |    2   
   2  1m00.6s
  ADTypes.AutoEnzyme(mode=EnzymeCore.ForwardMode{false, EnzymeCore.FFIABI, 
false, false, false}())                                                    
                                                                           
                                                                           
                                                                  |    2   
   2  1m06.8s
  ADTypes.AutoMooncake()                                                   
                                                                           
                                                                           
                                                                           
                                                                  |    2   
   2    55.2s
  ADTypes.AutoForwardDiff()                                                
                                                                           
                                                                           
                                                                           
                                                                  |    2   
   2     4.6s
  ADTypes.AutoSparse(dense_ad=ADTypes.AutoForwardDiff(), sparsity_detector=
SparseConnectivityTracer.TracerSparsityDetector(), coloring_algorithm=Spars
eMatrixColorings.GreedyColoringAlgorithm{:direct, 1, Tuple{SparseMatrixColo
rings.NaturalOrder}}((SparseMatrixColorings.NaturalOrder(),), false))      
                                                                  |    2   
   2     5.3s
  ADTypes.AutoSparse(dense_ad=ADTypes.AutoEnzyme(mode=EnzymeCore.ForwardMod
e{false, EnzymeCore.FFIABI, false, false, false}()), sparsity_detector=Spar
seConnectivityTracer.TracerSparsityDetector(), coloring_algorithm=SparseMat
rixColorings.GreedyColoringAlgorithm{:direct, 1, Tuple{SparseMatrixColoring
s.NaturalOrder}}((SparseMatrixColorings.NaturalOrder(),), false)) |    2   
   2     4.3s

backend	scenario	operator	prepared	calls	samples	evals	time	allocs	bytes	gc_fraction	compile_fraction
AutoEnzyme(mode=ReverseMode{false, false, false, FFIABI, false, false}())	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	valueandjacobian	1.0e+00	6.4e+01	5.0e+00	1.0e+00	1.7e-01	6.6e+03	2.8e+08	4.8e-01	0.0e+00
AutoEnzyme(mode=ReverseMode{false, false, false, FFIABI, false, false}())	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	jacobian	1.0e+00	6.3e+01	6.0e+00	1.0e+00	1.0e-01	6.6e+03	2.8e+08	3.2e-01	0.0e+00
AutoEnzyme(mode=ForwardMode{false, FFIABI, false, false, false}())	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	valueandjacobian	1.0e+00	6.3e+01	4.4e+01	1.0e+00	5.5e-03	5.3e+03	1.8e+07	0.0e+00	0.0e+00
AutoEnzyme(mode=ForwardMode{false, FFIABI, false, false, false}())	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	jacobian	1.0e+00	6.3e+01	3.0e+01	1.0e+00	5.6e-03	5.3e+03	1.8e+07	0.0e+00	0.0e+00
AutoMooncake()	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	valueandjacobian	1.0e+00	1.0e+00	1.1e+01	1.0e+00	7.2e-02	1.1e+04	3.3e+07	0.0e+00	0.0e+00
AutoMooncake()	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	jacobian	1.0e+00	0.0e+00	1.1e+01	1.0e+00	7.0e-02	1.1e+04	3.3e+07	0.0e+00	0.0e+00
AutoForwardDiff()	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	valueandjacobian	1.0e+00	8.5e+01	7.9e+01	1.0e+00	3.8e-03	2.6e+02	1.7e+07	0.0e+00	0.0e+00
AutoForwardDiff()	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	jacobian	1.0e+00	8.4e+01	1.3e+02	1.0e+00	3.8e-03	2.6e+02	1.7e+07	0.0e+00	0.0e+00
AutoSparse(densead=AutoForwardDiff(), sparsitydetector=TracerSparsityDetector(), coloring_algorithm=GreedyColoringAlgorithm{:direct, 1, Tuple{NaturalOrder}}((NaturalOrder(),), false))	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	valueandjacobian	1.0e+00	2.0e+00	1.5e+04	1.0e+00	2.0e-05	1.5e+01	9.6e+04	0.0e+00	0.0e+00
AutoSparse(densead=AutoForwardDiff(), sparsitydetector=TracerSparsityDetector(), coloring_algorithm=GreedyColoringAlgorithm{:direct, 1, Tuple{NaturalOrder}}((NaturalOrder(),), false))	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	jacobian	1.0e+00	1.0e+00	2.0e+04	1.0e+00	1.7e-05	1.2e+01	8.8e+04	0.0e+00	0.0e+00
AutoSparse(densead=AutoEnzyme(mode=ForwardMode{false, FFIABI, false, false, false}()), sparsitydetector=TracerSparsityDetector(), coloring_algorithm=GreedyColoringAlgorithm{:direct, 1, Tuple{NaturalOrder}}((NaturalOrder(),), false))	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	valueandjacobian	1.0e+00	2.0e+00	1.1e+04	1.0e+00	2.0e-05	2.3e+01	9.7e+04	0.0e+00	0.0e+00
AutoSparse(densead=AutoEnzyme(mode=ForwardMode{false, FFIABI, false, false, false}()), sparsitydetector=TracerSparsityDetector(), coloring_algorithm=GreedyColoringAlgorithm{:direct, 1, Tuple{NaturalOrder}}((NaturalOrder(),), false))	Scenario{:jacobian,:out} Diffusion : Vector{Float64} -\> Vector{Float64}	jacobian	1.0e+00	1.0e+00	1.8e+04	1.0e+00	1.5e-05	2.0e+01	8.9e+04	0.0e+00	0.0e+00

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/AutomaticDifferentiationSparse","ManualLoopDiffusionSparseAD.jmd")

Computer Information:

Julia Version 1.12.7
Commit 6d172b025e4 (2026-08-15 08:05 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver2)
  GC: Built with stock GC
Threads: 128 default, 1 interactive, 128 GC (on 128 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

Package Information:

Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/AutomaticDifferentiationSparse/Project.toml`
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  [a0c0ee7d] DifferentiationInterface v0.7.21
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⌃ [7da242da] Enzyme v0.13.199
⌃ [f6369f11] ForwardDiff v1.4.5
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⌃ [0a514795] SparseMatrixColorings v0.4.27
⌃ [0c5d862f] Symbolics v7.39.0
  [44d3d7a6] Weave v0.10.12
⌃ [e88e6eb3] Zygote v0.7.12
  [37e2e46d] LinearAlgebra v1.12.0
  [2f01184e] SparseArrays v1.12.0
  [8dfed614] Test v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

And the full manifest:

Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/AutomaticDifferentiationSparse/Manifest.toml`
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  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.4+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
  [a4ae2306] libaom_jll v3.14.1+0
  [0ac62f75] libass_jll v0.17.5+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [8e53e030] libdrm_jll v2.4.134+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.58+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.7.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.1+2
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.6+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`