Oval2 Long Run

using StochasticDiffEq, SDEProblemLibrary, Random
import OrdinaryDiffEqCore: PIController
prob = SDEProblemLibrary.oval2ModelExample(largeFluctuations=true,useBigs=false)

SDEProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: false
timespan: (0.0, 500.0)
u0: 19-element Vector{Float64}:
   0.128483
   1.256853
   0.0030203
   0.0027977
   0.0101511
   0.0422942
   0.2391346
   0.0008014
   0.0001464
   2.67e-5
   4.8e-6
   9.0e-7
   0.0619917
   1.2444292
   0.0486676
 199.9383546
 137.4267984
   1.5180203
   1.5180203

Random.seed!(250)
prob = remake(prob,tspan = (0.0,500.0))
sol = solve(prob,SOSRI(),dt=(1/2)^(18),progress=true,
          saveat=0.1,abstol=1e-5,reltol=1e-3,maxiters=1e7,force_dtmin=true,
          controller=PIController(SOSRI(); qmax=1.125));
Random.seed!(250)
prob = remake(prob,tspan = (0.0,500.0))
@time sol = solve(prob,SOSRI(),dt=(1/2)^(18),progress=true,
    saveat=0.1,abstol=1e-5,reltol=1e-3,maxiters=1e7,force_dtmin=true,
    controller=PIController(SOSRI(); qmax=1.125));

12.131854 seconds (126.70 k allocations: 12.854 MiB, 1.07% gc time)

println(maximum(@view sol[2, :]))
using Plots; gr()
lw = 2
lw2 = 3
p1 = plot(sol,idxs=(0,16),
          title="(A) Timeseries of Ecad Concentration",xguide="Time (s)",
          yguide="Concentration",guidefont=font(16),tickfont=font(16),
          linewidth=lw,leg=false)

28.92793713361406

p2 = plot(sol,idxs=(0,17),
          title="(B) Timeseries of Vim Concentration",xguide="Time (s)",
          yguide="Concentration",guidefont=font(16),
          tickfont=font(16),linewidth=lw,leg=false)

prob = remake(prob,tspan = (0.0,1.0))
## Little Run
sol = solve(prob,EM(),dt=(1/2)^(20),
          progress=true,saveat=0.1)
println("EM")
@time sol = solve(prob,EM(),dt=(1/2)^(20),
          progress=true,saveat=0.1)

sol = solve(prob,SRI(),dt=(1/2)^(18),adaptive=false,
            progress=true,save_everystep=false)
println("SRI")
@time sol = solve(prob,SRI(),dt=(1/2)^(18),adaptive=false,
          progress=true,save_everystep=false)

sol = solve(prob,SRIW1(),dt=(1/2)^(18),adaptive=false,
          progress=false,saveat=0.1)
println("SRIW1")
@time sol = solve(prob,SRIW1(),dt=(1/2)^(18),adaptive=false,
          progress=false,saveat=0.1)

sol = solve(prob,SRI(),dt=(1/2)^(18),
          progress=false,force_dtmin=true,
          saveat=0.1,abstol=1e-6,reltol=1e-4,
          controller=PIController(SRI(); qmax=1.125))
println("SRI Adaptive")
@time sol = solve(prob,SRI(),dt=(1/2)^(18),
          progress=false,force_dtmin=true,
          saveat=0.1,abstol=1e-6,reltol=1e-4,
          controller=PIController(SRI(); qmax=1.125))
@show length(sol.t)

sol = solve(prob,SRIW1(),dt=(1/2)^(18),
          progress=false,force_dtmin=true,
          saveat=0.1,abstol=1e-6,reltol=1e-4,
          controller=PIController(SRIW1(); qmax=1.125))
println("SRIW1 Adaptive")
@time sol = solve(prob,SRIW1(),dt=(1/2)^(18),
          progress=false,force_dtmin=true,
          saveat=0.1,abstol=1e-6,reltol=1e-4,
          controller=PIController(SRIW1(); qmax=1.125))
@show length(sol.t)

EM
  0.491690 seconds (124 allocations: 14.844 KiB)
SRI
  0.558882 seconds (347 allocations: 38.781 KiB)
SRIW1
  0.221304 seconds (181 allocations: 21.609 KiB)
SRI Adaptive
  0.591538 seconds (601 allocations: 64.062 KiB)
length(sol.t) = 11
SRIW1 Adaptive
  0.019293 seconds (431 allocations: 46.734 KiB)
length(sol.t) = 11
11

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/StiffSDE","Oval2LongRun.jmd")

Computer Information:

Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 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-16.0.6 (ORCJIT, znver2)
Threads: 128 default, 0 interactive, 64 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/StiffSDE/Project.toml`
  [f3b72e0c] DiffEqDevTools v3.2.0
⌃ [77a26b50] DiffEqNoiseProcess v5.34.0
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⌃ [bbf590c4] OrdinaryDiffEqCore v4.13.0
  [91a5bcdd] Plots v1.41.6
  [c72e72a9] SDEProblemLibrary v1.2.3
⌅ [0bca4576] SciMLBase v3.43.0
⌃ [31c91b34] SciMLBenchmarks v0.1.3
  [a6db7da4] SciMLLogging v2.0.4
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  [789caeaf] StochasticDiffEq v7.1.4
  [37e2e46d] LinearAlgebra v1.11.0
  [9a3f8284] Random v1.11.0
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`

And the full manifest:

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  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [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 v1.11.0
  [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 v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
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`