GitHub

Adaptive Efficiency Tests

using StochasticDiffEq, SDEProblemLibrary, DiffEqNoiseProcess, DiffEqBase, Plots
import SDEProblemLibrary: prob_sde_additive,
                          prob_sde_linear, prob_sde_wave

p1 = Vector{Any}(undef, 3)
p2 = Vector{Any}(undef, 3)
p3 = Vector{Any}(undef, 3)

probs = Matrix{SDEProblem}(undef, 3, 3)
## Problem 1
prob = prob_sde_linear
probs[1, 1] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM1)))
probs[1, 2] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM2)))
probs[1, 3] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM3)))
## Problem 2
prob = prob_sde_wave
probs[2, 1] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM1)))
probs[2, 2] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM2)))
probs[2, 3] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM3)))
## Problem 3
prob = prob_sde_additive
probs[3, 1] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM1)))
probs[3, 2] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM2)))
probs[3, 3] = SDEProblem(prob.f, prob.g, prob.u0, prob.tspan, prob.p,
    noise = WienerProcess(0.0, 0.0, 0.0, rswm = RSWM(adaptivealg = :RSwM3)))

fullMeans = Vector{Array}(undef, 3)
fullMedians = Vector{Array}(undef, 3)
fullElapsed = Vector{Array}(undef, 3)
fullTols = Vector{Array}(undef, 3)
offset = 0

Ns = [17, 23,
    17]
3-element Vector{Int64}:
 17
 23
 17

The Monte Carlo runs use multithreaded ensembles (EnsembleThreads()), so start Julia with multiple threads (e.g. julia -t auto) for parallel timing.

for k in 1:size(probs, 1)
    global probs, Ns, fullMeans, fullMedians, fullElapsed, fullTols
    println("Problem $k")
    ## Setup
    N = Ns[k]

    msims = Vector{Any}(undef, N)
    elapsed = Array{Float64}(undef, N, 3)
    medians = Array{Float64}(undef, N, 3)
    means = Array{Float64}(undef, N, 3)
    tols = Array{Float64}(undef, N, 3)

    #Compile
    prob = probs[k, 1]
    monte_prob = EnsembleProblem(prob)
    solve(monte_prob, SRIW1(), EnsembleThreads(), dt = 1/2^(4), adaptive = true,
        trajectories = 1000, abstol = 2.0^(-1), reltol = 0)

    println("RSwM1")
    for i in (1 + offset):(N + offset)
        tols[i - offset, 1] = 2.0^(-i-1)
        msims[i - offset] = DiffEqBase.calculate_ensemble_errors(solve(monte_prob, SRIW1(),
            EnsembleThreads(), trajectories = 1000, abstol = 2.0^(-i-1),
            reltol = 0, force_dtmin = true, maxiters = Int(1e7)))
        elapsed[i - offset, 1] = msims[i - offset].elapsedTime
        medians[i - offset, 1] = msims[i - offset].error_medians[:final]
        means[i - offset, 1] = msims[i - offset].error_means[:final]
    end

    println("RSwM2")
    prob = probs[k, 2]

    monte_prob = EnsembleProblem(prob)
    solve(monte_prob, SRIW1(), EnsembleThreads(), dt = 1/2^(4), adaptive = true,
        trajectories = 1000, abstol = 2.0^(-1), reltol = 0)

    for i in (1 + offset):(N + offset)
        tols[i - offset, 2] = 2.0^(-i-1)
        msims[i - offset] = DiffEqBase.calculate_ensemble_errors(solve(monte_prob, SRIW1(),
            EnsembleThreads(), trajectories = 1000, abstol = 2.0^(-i-1),
            reltol = 0, force_dtmin = true, maxiters = Int(1e7)))
        elapsed[i - offset, 2] = msims[i - offset].elapsedTime
        medians[i - offset, 2] = msims[i - offset].error_medians[:final]
        means[i - offset, 2] = msims[i - offset].error_means[:final]
    end

    println("RSwM3")
    prob = probs[k, 3]
    monte_prob = EnsembleProblem(prob)
    solve(monte_prob, SRIW1(), EnsembleThreads(), dt = 1/2^(4), adaptive = true,
        trajectories = 1000, abstol = 2.0^(-1), reltol = 0)

    for i in (1 + offset):(N + offset)
        tols[i - offset, 3] = 2.0^(-i-1)
        msims[i - offset] = DiffEqBase.calculate_ensemble_errors(solve(monte_prob, SRIW1(),
            EnsembleThreads(), adaptive = true, trajectories = 1000, abstol = 2.0^(-i-1),
            reltol = 0, force_dtmin = true, maxiters = Int(1e7)))
        elapsed[i - offset, 3] = msims[i - offset].elapsedTime
        medians[i - offset, 3] = msims[i - offset].error_medians[:final]
        means[i - offset, 3] = msims[i - offset].error_means[:final]
    end

    fullMeans[k] = means
    fullMedians[k] = medians
    fullElapsed[k] = elapsed
    fullTols[k] = tols
end
Problem 1
RSwM1
RSwM2
RSwM3
Problem 2
RSwM1
RSwM2
RSwM3
Problem 3
RSwM1
RSwM2
RSwM3
gr(fmt = :svg)
lw=3
leg=["RSwM1" "RSwM2" "RSwM3"]

titleFontSize = 16
guideFontSize = 14
legendFontSize = 14
tickFontSize = 12

for k in 1:size(probs, 1)
    global probs, Ns, fullMeans, fullMedians, fullElapsed, fullTols
    p1[k] = Plots.plot(fullTols[k], fullMeans[k], xscale = :log10, yscale = :log10,
        xguide = "Absolute Tolerance", yguide = "Mean Final Error",
        title = "Example $k", linewidth = lw, grid = false, lab = leg,
        titlefont = font(titleFontSize), legendfont = font(legendFontSize),
        tickfont = font(tickFontSize), guidefont = font(guideFontSize))
    p2[k] = Plots.plot(fullTols[k], fullMedians[k], xscale = :log10, yscale = :log10,
        xguide = "Absolute Tolerance", yguide = "Median Final Error",
        title = "Example $k", linewidth = lw, grid = false, lab = leg,
        titlefont = font(titleFontSize), legendfont = font(legendFontSize),
        tickfont = font(tickFontSize), guidefont = font(guideFontSize))
    p3[k] = Plots.plot(fullTols[k], fullElapsed[k], xscale = :log10, yscale = :log10,
        xguide = "Absolute Tolerance", yguide = "Elapsed Time",
        title = "Example $k", linewidth = lw, grid = false, lab = leg,
        titlefont = font(titleFontSize), legendfont = font(legendFontSize),
        tickfont = font(tickFontSize), guidefont = font(guideFontSize))
end

Plots.plot!(p1[1])
Plots.plot(p1[1], p1[2], p1[3], layout = (3, 1), size = (1000, 800))

#savefig("meanvstol.png")
#savefig("meanvstol.pdf")
plot(p3[1], p3[2], p3[3], layout = (3, 1), size = (1000, 800))
#savefig("timevstol.png")
#savefig("timevstol.pdf")

plot(p1[1], p3[1], p1[2], p3[2], p1[3], p3[3], layout = (3, 2), size = (1000, 800))


using SciMLBenchmarks
SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder], WEAVE_ARGS[:file])

Appendix

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/AdaptiveSDE","AdaptiveEfficiencyTests.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_DEPOT_PATH = /home/crackauc/github-runners/amdci8-1/.julia
  JULIA_NUM_THREADS = auto

Package Information:

Status `~/github-runners/amdci8-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/AdaptiveSDE/Project.toml`
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⌃ [bbf590c4] OrdinaryDiffEqCore v4.17.2
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  [a6db7da4] SciMLLogging v2.1.0
  [789caeaf] StochasticDiffEq v7.2.0
  [9a3f8284] Random v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

And the full manifest:

Status `~/github-runners/amdci8-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/AdaptiveSDE/Manifest.toml`
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  [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
  [1317d2d5] oneTBB_jll v2022.3.0+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
  [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 v1.3.0+1
  [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 v3.5.4+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`