qmax Determination

qs = 1.0 .+ 2.0.^(-5:2)
times = Array{Float64}(undef,length(qs),4)
means = Array{Float64}(undef,length(qs),4)

using StochasticDiffEq, SDEProblemLibrary, Random,
      Plots, ParallelDataTransfer, DiffEqMonteCarlo, Distributed
Random.seed!(99)

full_prob = SDEProblemLibrary.oval2ModelExample(largeFluctuations=true,useBigs=false)
import SDEProblemLibrary: prob_sde_additivesystem,
            prob_sde_additive, prob_sde_2Dlinear, prob_sde_linear, prob_sde_wave
prob = remake(full_prob,tspan=(0.0,1.0))

println("Solve once to compile.")
sol = solve(prob,EM(),dt=1/2^(18))
Int(sol.u[end][1]!=NaN)
println("Compilation complete.")
num_runs = 10000

probs = Vector{SDEProblem}(undef,3)
p1 = Vector{Any}(undef,3)
p2 = Vector{Any}(undef,3)
p3 = Vector{Any}(undef,3)
## Problem 1
probs[1] = prob_sde_linear
## Problem 2
probs[2] = prob_sde_wave
## Problem 3
probs[3] = prob_sde_additive

println("Setup Complete")

## Timing Runs

function runAdaptive(i,k)
  sol = solve(prob,SRIW1(),dt=1/2^(8),abstol=2.0^(-15),reltol=2.0^(-10),
              verbose=false,maxIters=Int(1e12),qmax=qs[k])
  Int(any(isnan,sol[end]) || sol.t[end] != 1)
end

#Compile
monte_prob = EnsembleProblem(probs[1])
test_mc = solve(monte_prob,SRIW1(),dt=1/2^(4),adaptive=true,trajectories=1000,abstol=2.0^(-1),reltol=0)
DiffEqBase.calculate_monte_errors(test_mc);

Error: On worker 2:
ArgumentError: Package SDEProblemLibrary [c72e72a9-a271-4b2b-8966-303ed9567
72e] is required but does not seem to be installed:
 - Run `Pkg.instantiate()` to install all recorded dependencies.

Stacktrace:
 [1] _require
   @ ./loading.jl:1089
 [2] require
   @ ./loading.jl:1013
 [3] #2
   @ /cache/julia-buildkite-plugin/julia_installs/bin/linux/x64/1.7/julia-1
.7-latest-linux-x86_64/share/julia/stdlib/v1.7/Distributed/src/Distributed.
jl:79
 [4] #114
   @ /cache/julia-buildkite-plugin/julia_installs/bin/linux/x64/1.7/julia-1
.7-latest-linux-x86_64/share/julia/stdlib/v1.7/Distributed/src/process_mess
ages.jl:294
 [5] run_work_thunk
   @ /cache/julia-buildkite-plugin/julia_installs/bin/linux/x64/1.7/julia-1
.7-latest-linux-x86_64/share/julia/stdlib/v1.7/Distributed/src/process_mess
ages.jl:63
 [6] run_work_thunk
   @ /cache/julia-buildkite-plugin/julia_installs/bin/linux/x64/1.7/julia-1
.7-latest-linux-x86_64/share/julia/stdlib/v1.7/Distributed/src/process_mess
ages.jl:72
 [7] #100
   @ ./task.jl:429

...and 1 more exception.

qmax test on Oval2 Model

for k in eachindex(qs)
  global times
  Random.seed!(99)
  adaptiveTime = @elapsed numFails = sum(map((i)->runAdaptive(i,k),1:num_runs))
  println("k was $k. The number of Adaptive Fails is $numFails. Elapsed time was $adaptiveTime")
  times[k,4] = adaptiveTime
end

Error: UndefVarError: Random not defined

qmax test on other problems

for k in eachindex(probs)
  global probs, times, means, qs
  println("Problem $k")
  ## Setup
  prob = probs[k]

  for i in eachindex(qs)
    msim = solve(monte_prob,dt=1/2^(4),SRIW1(),adaptive=true,trajectories=num_runs,abstol=2.0^(-13),reltol=0,qmax=qs[i])
    test_msim = DiffEqBase.calculate_monte_errors(msim)
    times[i,k] = test_msim.elapsedTime
    means[i,k] = test_msim.error_means[:final]
    println("for k=$k and i=$i, we get that the error was $(means[i,k]) and it took $(times[i,k]) seconds")
  end
end

Error: UndefVarError: probs not defined

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","qmaxDetermination.jmd")

Computer Information:

Julia Version 1.7.3
Commit 742b9abb4d (2022-05-06 12:58 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-12.0.1 (ORCJIT, znver2)
Environment:
  JULIA_CPU_THREADS = 128
  BUILDKITE_PLUGIN_JULIA_CACHE_DIR = /cache/julia-buildkite-plugin
  JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953

Package Information:

      Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/AdaptiveSDE/Project.toml`
  [77a26b50] DiffEqNoiseProcess v5.13.0
  [2dcacdae] ParallelDataTransfer v0.5.0
  [91a5bcdd] Plots v1.34.0
  [c72e72a9] SDEProblemLibrary v0.1.3
  [31c91b34] SciMLBenchmarks v0.1.1
  [789caeaf] StochasticDiffEq v6.54.0
  [8ba89e20] Distributed
  [9a3f8284] Random

And the full manifest:

      Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/AdaptiveSDE/Manifest.toml`
  [c3fe647b] AbstractAlgebra v0.27.4
  [1520ce14] AbstractTrees v0.4.2
  [79e6a3ab] Adapt v3.4.0
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.2.0
  [4fba245c] ArrayInterface v6.0.23
  [30b0a656] ArrayInterfaceCore v0.1.20
  [6ba088a2] ArrayInterfaceGPUArrays v0.2.2
  [015c0d05] ArrayInterfaceOffsetArrays v0.1.6
  [b0d46f97] ArrayInterfaceStaticArrays v0.1.4
  [dd5226c6] ArrayInterfaceStaticArraysCore v0.1.0
  [15f4f7f2] AutoHashEquals v0.2.0
  [198e06fe] BangBang v0.3.37
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.4
  [d1d4a3ce] BitFlags v0.1.5
  [62783981] BitTwiddlingConvenienceFunctions v0.1.4
  [2a0fbf3d] CPUSummary v0.1.27
  [00ebfdb7] CSTParser v3.3.6
  [49dc2e85] Calculus v0.5.1
  [479239e8] Catalyst v12.3.0
  [d360d2e6] ChainRulesCore v1.15.6
  [9e997f8a] ChangesOfVariables v0.1.4
  [fb6a15b2] CloseOpenIntervals v0.1.10
  [944b1d66] CodecZlib v0.7.0
  [35d6a980] ColorSchemes v3.19.0
  [3da002f7] ColorTypes v0.11.4
  [c3611d14] ColorVectorSpace v0.9.9
  [5ae59095] Colors v0.12.8
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.6
  [38540f10] CommonSolve v0.2.1
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.2.0
  [b152e2b5] CompositeTypes v0.1.2
  [a33af91c] CompositionsBase v0.1.1
  [8f4d0f93] Conda v1.7.0
  [187b0558] ConstructionBase v1.4.1
  [d38c429a] Contour v0.6.2
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.11.0
  [864edb3b] DataStructures v0.18.13
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [b429d917] DensityInterface v0.4.0
  [2b5f629d] DiffEqBase v6.105.0
  [459566f4] DiffEqCallbacks v2.24.1
  [77a26b50] DiffEqNoiseProcess v5.13.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.11.1
  [b4f34e82] Distances v0.10.7
  [31c24e10] Distributions v0.25.75
  [ffbed154] DocStringExtensions v0.8.6
  [5b8099bc] DomainSets v0.5.13
  [fa6b7ba4] DualNumbers v0.6.8
  [7c1d4256] DynamicPolynomials v0.4.5
  [d4d017d3] ExponentialUtilities v1.19.0
  [e2ba6199] ExprTools v0.1.8
  [c87230d0] FFMPEG v0.4.1
  [7034ab61] FastBroadcast v0.2.1
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v1.2.7
  [1a297f60] FillArrays v0.13.4
  [6a86dc24] FiniteDiff v2.15.0
  [53c48c17] FixedPointNumbers v0.8.4
  [59287772] Formatting v0.4.2
  [f6369f11] ForwardDiff v0.10.32
  [069b7b12] FunctionWrappers v1.1.2
  [77dc65aa] FunctionWrappersWrappers v0.1.1
  [46192b85] GPUArraysCore v0.1.2
  [28b8d3ca] GR v0.68.0
  [c145ed77] GenericSchur v0.5.3
  [d7ba0133] Git v1.2.1
  [86223c79] Graphs v1.7.4
  [42e2da0e] Grisu v1.0.2
  [0b43b601] Groebner v0.2.10
  [d5909c97] GroupsCore v0.4.0
  [cd3eb016] HTTP v1.4.0
  [eafb193a] Highlights v0.4.5
  [3e5b6fbb] HostCPUFeatures v0.1.8
  [34004b35] HypergeometricFunctions v0.3.11
  [7073ff75] IJulia v1.23.3
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.3
  [83e8ac13] IniFile v0.5.1
  [22cec73e] InitialValues v0.3.1
  [18e54dd8] IntegerMathUtils v0.1.0
  [8197267c] IntervalSets v0.7.2
  [3587e190] InverseFunctions v0.1.7
  [92d709cd] IrrationalConstants v0.1.1
  [42fd0dbc] IterativeSolvers v0.9.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.5
  [692b3bcd] JLLWrappers v1.4.1
  [682c06a0] JSON v0.21.3
  [98e50ef6] JuliaFormatter v1.0.10
  [ccbc3e58] JumpProcesses v9.2.0
  [ef3ab10e] KLU v0.3.0
  [ba0b0d4f] Krylov v0.8.4
  [0b1a1467] KrylovKit v0.5.4
  [b964fa9f] LaTeXStrings v1.3.0
  [2ee39098] LabelledArrays v1.12.0
  [23fbe1c1] Latexify v0.15.17
  [10f19ff3] LayoutPointers v0.1.10
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v1.26.0
  [2ab3a3ac] LogExpFunctions v0.3.18
  [e6f89c97] LoggingExtras v0.4.9
  [bdcacae8] LoopVectorization v0.12.128
  [1914dd2f] MacroTools v0.5.9
  [d125e4d3] ManualMemory v0.1.8
  [739be429] MbedTLS v1.1.6
  [442fdcdd] Measures v0.3.1
  [e9d8d322] Metatheory v1.3.5
  [128add7d] MicroCollections v0.1.2
  [e1d29d7a] Missings v1.0.2
  [961ee093] ModelingToolkit v8.23.0
  [46d2c3a1] MuladdMacro v0.2.2
  [102ac46a] MultivariatePolynomials v0.4.6
  [ffc61752] Mustache v1.0.14
  [d8a4904e] MutableArithmetics v1.0.4
  [d41bc354] NLSolversBase v7.8.2
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.1
  [8913a72c] NonlinearSolve v0.3.22
  [6fe1bfb0] OffsetArrays v1.12.7
  [4d8831e6] OpenSSL v1.1.2
  [429524aa] Optim v1.7.3
  [bac558e1] OrderedCollections v1.4.1
  [1dea7af3] OrdinaryDiffEq v6.27.2
  [90014a1f] PDMats v0.11.16
  [2dcacdae] ParallelDataTransfer v0.5.0
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.4.0
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.0.0
  [995b91a9] PlotUtils v1.3.1
  [91a5bcdd] Plots v1.34.0
  [e409e4f3] PoissonRandom v0.4.1
  [f517fe37] Polyester v0.6.15
  [1d0040c9] PolyesterWeave v0.1.10
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.4
  [21216c6a] Preferences v1.3.0
  [27ebfcd6] Primes v0.5.3
  [1fd47b50] QuadGK v2.5.0
  [74087812] Random123 v1.6.0
  [fb686558] RandomExtensions v0.4.3
  [e6cf234a] RandomNumbers v1.5.3
  [3cdcf5f2] RecipesBase v1.2.1
  [01d81517] RecipesPipeline v0.6.3
  [731186ca] RecursiveArrayTools v2.32.0
  [f2c3362d] RecursiveFactorization v0.2.12
  [189a3867] Reexport v1.2.2
  [42d2dcc6] Referenceables v0.1.2
  [05181044] RelocatableFolders v1.0.0
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.7.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.3
  [c72e72a9] SDEProblemLibrary v0.1.3
  [3cdde19b] SIMDDualNumbers v0.1.1
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.35
  [0bca4576] SciMLBase v1.59.3
  [31c91b34] SciMLBenchmarks v0.1.1
  [6c6a2e73] Scratch v1.1.1
  [efcf1570] Setfield v0.8.2
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.1.0
  [699a6c99] SimpleTraits v0.9.4
  [66db9d55] SnoopPrecompile v1.0.1
  [b85f4697] SoftGlobalScope v1.1.0
  [a2af1166] SortingAlgorithms v1.0.1
  [47a9eef4] SparseDiffTools v1.26.2
  [276daf66] SpecialFunctions v2.1.7
  [171d559e] SplittablesBase v0.1.14
  [aedffcd0] Static v0.7.7
  [90137ffa] StaticArrays v1.5.8
  [1e83bf80] StaticArraysCore v1.4.0
  [82ae8749] StatsAPI v1.5.0
  [2913bbd2] StatsBase v0.33.21
  [4c63d2b9] StatsFuns v1.0.1
  [789caeaf] StochasticDiffEq v6.54.0
  [7792a7ef] StrideArraysCore v0.3.15
  [69024149] StringEncodings v0.3.5
  [d1185830] SymbolicUtils v0.19.11
  [0c5d862f] Symbolics v4.10.4
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.9.0
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v0.2.3
  [8290d209] ThreadingUtilities v0.5.0
  [ac1d9e8a] ThreadsX v0.1.10
  [a759f4b9] TimerOutputs v0.5.21
  [0796e94c] Tokenize v0.5.24
  [3bb67fe8] TranscodingStreams v0.9.9
  [28d57a85] Transducers v0.4.73
  [a2a6695c] TreeViews v0.3.0
  [d5829a12] TriangularSolve v0.1.14
  [410a4b4d] Tricks v0.1.6
  [5c2747f8] URIs v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.12.0
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.49
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [44d3d7a6] Weave v0.10.9
  [ddb6d928] YAML v0.4.7
  [c2297ded] ZMQ v1.2.1
  [700de1a5] ZygoteRules v0.2.2
  [6e34b625] Bzip2_jll v1.0.8+0
  [83423d85] Cairo_jll v1.16.1+1
  [2e619515] Expat_jll v2.4.8+0
  [b22a6f82] FFMPEG_jll v4.4.2+0
  [a3f928ae] Fontconfig_jll v2.13.93+0
  [d7e528f0] FreeType2_jll v2.10.4+0
  [559328eb] FriBidi_jll v1.0.10+0
  [0656b61e] GLFW_jll v3.3.8+0
  [d2c73de3] GR_jll v0.69.0+0
  [78b55507] Gettext_jll v0.21.0+0
  [f8c6e375] Git_jll v2.34.1+0
  [7746bdde] Glib_jll v2.68.3+2
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [aacddb02] JpegTurbo_jll v2.1.2+0
  [c1c5ebd0] LAME_jll v3.100.1+0
  [88015f11] LERC_jll v3.0.0+1
  [dd4b983a] LZO_jll v2.10.1+0
  [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.7+0
  [7e76a0d4] Libglvnd_jll v1.3.0+3
  [7add5ba3] Libgpg_error_jll v1.42.0+0
  [94ce4f54] Libiconv_jll v1.16.1+1
  [4b2f31a3] Libmount_jll v2.35.0+0
  [89763e89] Libtiff_jll v4.4.0+0
  [38a345b3] Libuuid_jll v2.36.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v1.1.17+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [2f80f16e] PCRE_jll v8.44.0+0
  [30392449] Pixman_jll v0.40.1+0
  [ea2cea3b] Qt5Base_jll v5.15.3+1
  [f50d1b31] Rmath_jll v0.3.0+0
  [a2964d1f] Wayland_jll v1.19.0+0
  [2381bf8a] Wayland_protocols_jll v1.25.0+0
  [02c8fc9c] XML2_jll v2.9.14+0
  [aed1982a] XSLT_jll v1.1.34+0
  [4f6342f7] Xorg_libX11_jll v1.6.9+4
  [0c0b7dd1] Xorg_libXau_jll v1.0.9+4
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.3+4
  [1082639a] Xorg_libXext_jll v1.3.4+4
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.10+4
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.0+3
  [c7cfdc94] Xorg_libxcb_jll v1.13.0+3
  [cc61e674] Xorg_libxkbfile_jll v1.1.0+4
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.2+4
  [33bec58e] Xorg_xkeyboard_config_jll v2.27.0+4
  [c5fb5394] Xorg_xtrans_jll v1.4.0+3
  [8f1865be] ZeroMQ_jll v4.3.4+0
  [3161d3a3] Zstd_jll v1.5.2+0
  [214eeab7] fzf_jll v0.29.0+0
  [a4ae2306] libaom_jll v3.4.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [b53b4c65] libpng_jll v1.6.38+0
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8bb1440f] DelimitedFiles
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [b27032c2] LibCURL v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.8.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.0
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v0.5.2+0
  [deac9b47] LibCURL_jll v7.84.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [c8ffd9c3] MbedTLS_jll v2.28.0+0
  [14a3606d] MozillaCACerts_jll v2022.2.1
  [4536629a] OpenBLAS_jll v0.3.20+0
  [05823500] OpenLibm_jll v0.8.1+0
  [efcefdf7] PCRE2_jll v10.40.0+0
  [bea87d4a] SuiteSparse_jll v5.10.1+0
  [83775a58] Zlib_jll v1.2.12+3
  [8e850b90] libblastrampoline_jll v5.1.1+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+0