Oval2 Timings

using StochasticDiffEq, SDEProblemLibrary, Random, Base.Threads
import OrdinaryDiffEqCore: PIController
using SciMLLogging
prob = SDEProblemLibrary.oval2ModelExample(largeFluctuations=true,useBigs=false)
prob_func(prob, ctx) = remake(prob, seed = ctx.sim_id)
prob = EnsembleProblem(remake(prob,tspan=(0.0,1.0)),prob_func=prob_func)
js = 16:21
dts = 1.0 ./ 2.0 .^ (js)
trajectories = 1000
fails = fill(-1, length(dts), 3)
times = fill(NaN, length(dts), 3)

6×3 Matrix{Float64}:
 NaN  NaN  NaN
 NaN  NaN  NaN
 NaN  NaN  NaN
 NaN  NaN  NaN
 NaN  NaN  NaN
 NaN  NaN  NaN

This page times 1000 trajectories of the Oval2 model on $t \in [0, 1]$. A trajectory counts as failed if its final state contains NaN or it stops before $t = 1$. The adaptive runs use several Rössler SRI methods. The fixed-step runs set adaptive = false and sweep $\Delta t = 2^{-16}, \dots, 2^{-21}$ ($2^{-17}, \dots, 2^{-21}$ for the implicit methods, $2^{-16}, \dots, 2^{-19}$ for SRIW1). The final plot shows the elapsed time of the explicit fixed-step methods against $\Delta t$, the fastest adaptive run without failures (dashed), and red dots at the largest $\Delta t$ at which each fixed-step method has no failed trajectories.

Timing Runs

sol = solve(prob,SRIW1(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-7),maxiters=Int(1e11), controller=PIController(SRIW1(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SRIW1(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-7),maxiters=Int(1e11), controller=PIController(SRIW1(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? Inf : adaptive_time
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 2.012135613

sol = solve(prob,SRI(error_terms=2),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-7),maxiters=Int(1e11), controller=PIController(SRI(error_terms=2); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SRI(error_terms=2),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-7),maxiters=Int(1e11), controller=PIController(SRI(error_terms=2); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 2.610441682

sol = solve(prob,SRI(),EnsembleThreads(),abstol=2.0^(-14),reltol=2.0^(-18),maxiters=Int(1e11), controller=PIController(SRI(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SRI(),EnsembleThreads(),abstol=2.0^(-14),reltol=2.0^(-18),maxiters=Int(1e11), controller=PIController(SRI(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 15.285509036

sol = solve(prob,SRI(tableau=StochasticDiffEq.constructSRIOpt1()),EnsembleThreads(),abstol=2.0^(-7),reltol=2.0^(-4),maxiters=Int(1e11), controller=PIController(SRI(tableau=StochasticDiffEq.constructSRIOpt1()); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SRI(tableau=StochasticDiffEq.constructSRIOpt1()),EnsembleThreads(),abstol=2.0^(-7),reltol=2.0^(-4),maxiters=Int(1e11), controller=PIController(SRI(tableau=StochasticDiffEq.constructSRIOpt1()); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 0.344245804

sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-7),reltol=2.0^(-4),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-7),reltol=2.0^(-4),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 0.122152328

sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-7),reltol=2.0^(-6),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-7),reltol=2.0^(-6),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 0.194258523

sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-12),reltol=2.0^(-15),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-12),reltol=2.0^(-15),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 1.319223633

sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-7),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-7),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 0.148400432

sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-12),reltol=2.0^(-15),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI(),EnsembleThreads(),abstol=2.0^(-12),reltol=2.0^(-15),maxiters=Int(1e11), controller=PIController(SOSRI(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 1.266465787

sol = solve(prob,SOSRI2(),EnsembleThreads(),abstol=2.0^(-12),reltol=2.0^(-15),maxiters=Int(1e11), controller=PIController(SOSRI2(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI2(),EnsembleThreads(),abstol=2.0^(-12),reltol=2.0^(-15),maxiters=Int(1e11), controller=PIController(SOSRI2(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 1.28377593

sol = solve(prob,SOSRI2(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-11),maxiters=Int(1e11), controller=PIController(SOSRI2(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI2(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-11),maxiters=Int(1e11), controller=PIController(SOSRI2(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 0.620237262

sol = solve(prob,SOSRI2(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-11),maxiters=Int(1e11), controller=PIController(SOSRI2(); qmax=1.125),save_everystep=false,trajectories=Threads.nthreads())
adaptive_time = @elapsed sol = solve(prob,SOSRI2(),EnsembleThreads(),abstol=2.0^(-13),reltol=2.0^(-11),maxiters=Int(1e11), controller=PIController(SOSRI2(); qmax=1.125),save_everystep=false,trajectories=trajectories)
numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
best_adaptive_time = numfails != 0 ? best_adaptive_time : min(best_adaptive_time,adaptive_time)
println("The number of Adaptive Fails is $numfails. Elapsed time was $adaptive_time")

The number of Adaptive Fails is 0. Elapsed time was 0.53356855

for j in eachindex(js)
  println("j = $j")
  sol =solve(prob,EM(),EnsembleThreads(),dt=dts[j],maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=Threads.nthreads())
  t1 = @elapsed sol = solve(prob,EM(),EnsembleThreads(),dt=dts[j],maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=trajectories)
  numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
  println("The number of Euler-Maruyama Fails is $numfails. Elapsed time was $t1")
  fails[j,1] = numfails
  times[j,1] = t1
end

j = 1
The number of Euler-Maruyama Fails is 10. Elapsed time was 0.633276961
j = 2
The number of Euler-Maruyama Fails is 1. Elapsed time was 1.08619304
j = 3
The number of Euler-Maruyama Fails is 1. Elapsed time was 2.01433507
j = 4
The number of Euler-Maruyama Fails is 0. Elapsed time was 4.030039675
j = 5
The number of Euler-Maruyama Fails is 0. Elapsed time was 7.628622838
j = 6
The number of Euler-Maruyama Fails is 0. Elapsed time was 15.155387504

for j in 1:4
  println("j = $j")
  sol =solve(prob,SRIW1(),EnsembleThreads(),dt=dts[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=Threads.nthreads())
  t1 = @elapsed sol = solve(prob,SRIW1(),EnsembleThreads(),dt=dts[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=trajectories)
  numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
  println("The number of SRIW1 Fails is $numfails. Elapsed time was $t1")
  fails[j,3] = numfails
  times[j,3] = t1
end

j = 1
The number of SRIW1 Fails is 8. Elapsed time was 1.036354435
j = 2
The number of SRIW1 Fails is 4. Elapsed time was 2.060052761
j = 3
The number of SRIW1 Fails is 2. Elapsed time was 4.114597771
j = 4
The number of SRIW1 Fails is 0. Elapsed time was 8.783841894

js_imp = 17:21
dts_imp = 1.0 ./ 2.0 .^ (js_imp)
for j in eachindex(dts_imp)
  println("j = $j")
  sol =solve(prob,ImplicitEM(),EnsembleThreads(),dt=dts_imp[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=Threads.nthreads())
  t1 = @elapsed sol = solve(prob,ImplicitEM(),EnsembleThreads(),dt=dts_imp[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=trajectories)
  numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
  println("The number of Implicit-EM Fails is $numfails. Elapsed time was $t1")
end

j = 1
The number of Implicit-EM Fails is 0. Elapsed time was 10.711856218
j = 2
The number of Implicit-EM Fails is 0. Elapsed time was 21.154694582
j = 3
The number of Implicit-EM Fails is 0. Elapsed time was 42.688374583
j = 4
The number of Implicit-EM Fails is 0. Elapsed time was 83.801006584
j = 5
The number of Implicit-EM Fails is 0. Elapsed time was 166.852625881

for j in eachindex(dts_imp)
  println("j = $j")
  sol =solve(prob,ImplicitRKMil(),EnsembleThreads(),dt=dts_imp[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=Threads.nthreads())
  t1 = @elapsed sol = solve(prob,ImplicitRKMil(),EnsembleThreads(),dt=dts_imp[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=trajectories)
  numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
  println("The number of Implicit-RKMil Fails is $numfails. Elapsed time was $t1")
end

j = 1
The number of Implicit-RKMil Fails is 0. Elapsed time was 10.665254272
j = 2
The number of Implicit-RKMil Fails is 0. Elapsed time was 21.231285575
j = 3
The number of Implicit-RKMil Fails is 0. Elapsed time was 43.497842073
j = 4
The number of Implicit-RKMil Fails is 0. Elapsed time was 86.982487849
j = 5
The number of Implicit-RKMil Fails is 0. Elapsed time was 180.302330708

for j in eachindex(dts)
  println("j = $j")
  sol =solve(prob,RKMil(),EnsembleThreads(),dt=dts[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=Threads.nthreads())
  t1 = @elapsed sol = solve(prob,RKMil(),EnsembleThreads(),dt=dts[j],adaptive=false,maxiters=Int(1e11),save_everystep=false,verbose=SciMLLogging.None(),trajectories=trajectories)
  numfails = sum([Int(any(isnan,sol.u[i]) || sol.u[i].t[end] != 1) for i in 1:trajectories])
  println("The number of RKMil Fails is $numfails. Elapsed time was $t1")
  fails[j,2] = numfails
  times[j,2] = t1
end

j = 1
The number of RKMil Fails is 10. Elapsed time was 0.608926355
j = 2
The number of RKMil Fails is 1. Elapsed time was 1.138232103
j = 3
The number of RKMil Fails is 1. Elapsed time was 2.311607662
j = 4
The number of RKMil Fails is 0. Elapsed time was 4.603748217
j = 5
The number of RKMil Fails is 0. Elapsed time was 8.355420456
j = 6
The number of RKMil Fails is 0. Elapsed time was 18.557083522

using Plots, LaTeXStrings
lw = 3
p2 = plot(dts,times,xscale=:log2,yscale=:log2,guidefont=font(16),tickfont=font(14),yguide="Elapsed Time (s)",xguide=L"Chosen $\Delta t$",linewidth=lw,lab=["Euler-Maruyama" "RK-Mil" "RosslerSRI"],legendfont=font(14))
plot!(dts,fill(best_adaptive_time, length(dts)),linewidth=lw,line=:dash,lab="ESRK+RSwM3")
stable = [findfirst(==(0), fails[:,i]) for i in 1:3]
stable_idxs = [(j,i) for (i,j) in enumerate(stable) if j !== nothing]
scatter!([dts[j] for (j,i) in stable_idxs],[times[j,i] for (j,i) in stable_idxs],markersize=20,c=:red,lab="")
plot(p2,size=(800,800))

Conclusion

In the latest run, Euler-Maruyama, RKMil, and SRIW1 all have failed trajectories for $\Delta t \geq 2^{-18}$ and first complete all 1000 trajectories at $\Delta t = 2^{-19}$. The implicit methods have no failures at any tested $\Delta t$, but are substantially slower than those cheapest stable fixed-step runs. Absolute wall-clock times vary with machine load; the qualitative ranking does not. The fastest adaptive run (SOSRI with abstol = 2^-7, reltol = 2^-4) completes all trajectories more than an order of magnitude faster than the cheapest fixed-step run without failures.

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","Oval2Timings.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_NUM_THREADS = auto

Package Information:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/StiffSDE/Project.toml`
  [f3b72e0c] DiffEqDevTools v3.6.3
  [77a26b50] DiffEqNoiseProcess v5.36.3
  [b964fa9f] LaTeXStrings v1.4.1
⌃ [bbf590c4] OrdinaryDiffEqCore v4.17.2
  [91a5bcdd] Plots v1.41.7
  [c72e72a9] SDEProblemLibrary v1.2.4
⌃ [0bca4576] SciMLBase v3.54.0
  [31c91b34] SciMLBenchmarks v0.2.1
  [a6db7da4] SciMLLogging v2.1.0
  [10745b16] Statistics v1.11.5
  [789caeaf] StochasticDiffEq v7.2.0
  [37e2e46d] LinearAlgebra v1.11.0
  [9a3f8284] Random v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

And the full manifest:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/StiffSDE/Manifest.toml`
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  [4fba245c] ArrayInterface v7.30.2
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⌃ [3da002f7] ColorTypes v0.12.1
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⌃ [5ae59095] Colors v0.13.1
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  [187b0558] ConstructionBase v1.6.0
  [d38c429a] Contour v0.6.3
  [a8cc5b0e] Crayons v4.2.0
  [9a962f9c] DataAPI v1.16.0
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  [8bb1440f] DelimitedFiles v1.9.1
⌃ [2b5f629d] DiffEqBase v7.21.1
  [459566f4] DiffEqCallbacks v4.19.4
  [f3b72e0c] DiffEqDevTools v3.6.3
  [77a26b50] DiffEqNoiseProcess v5.36.3
  [163ba53b] DiffResults v1.1.0
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  [a0c0ee7d] DifferentiationInterface v0.7.21
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⌃ [1a297f60] FillArrays v1.17.0
⌃ [64ca27bc] FindFirstFunctions v3.2.1
  [6a86dc24] FiniteDiff v2.33.0
⌅ [53c48c17] FixedPointNumbers v0.8.6
  [1fa38f19] Format v1.3.7
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  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v1.13.0
⌃ [46192b85] GPUArraysCore v0.2.0
  [28b8d3ca] GR v0.73.27
  [a0844989] Gamma v1.2.0
  [86223c79] Graphs v1.15.0
⌅ [eafb193a] Highlights v0.5.3
  [34004b35] HypergeometricFunctions v0.3.30
  [d25df0c9] Inflate v0.1.5
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.8.0
⌅ [682c06a0] JSON v0.21.4
⌃ [ccbc3e58] JumpProcesses v9.32.3
  [ba0b0d4f] Krylov v0.10.10
  [2faa5264] LHLFactorization v2.2.2
  [b964fa9f] LaTeXStrings v1.4.1
  [23fbe1c1] Latexify v0.16.12
  [87fe0de2] LineSearch v0.1.18
⌃ [7ed4a6bd] LinearSolve v5.17.3
⌃ [2ab3a3ac] LogExpFunctions v1.0.1
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [bb5d69b7] MaybeInplace v0.1.8
  [442fdcdd] Measures v0.3.3
  [e1d29d7a] Missings v1.2.0
  [46d2c3a1] MuladdMacro v0.2.7
⌃ [ffc61752] Mustache v1.0.21
  [77ba4419] NaNMath v1.1.4
⌃ [8913a72c] NonlinearSolve v4.30.0
⌃ [be0214bd] NonlinearSolveBase v2.49.5
⌃ [5959db7a] NonlinearSolveFirstOrder v2.6.1
  [9a2c21bd] NonlinearSolveQuasiNewton v1.15.3
  [26075421] NonlinearSolveSpectralMethods v1.8.3
  [bac558e1] OrderedCollections v2.0.1
⌃ [bbf590c4] OrdinaryDiffEqCore v4.17.2
⌃ [4302a76b] OrdinaryDiffEqDifferentiation v3.12.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.8
  [90014a1f] PDMats v0.11.41
⌅ [69de0a69] Parsers v2.8.8
  [ccf2f8ad] PlotThemes v3.3.0
⌃ [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.7
  [e409e4f3] PoissonRandom v0.4.13
  [d236fae5] PreallocationTools v1.7.1
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.6.0
  [08abe8d2] PrettyTables v3.4.8
  [43287f4e] PtrArrays v1.4.0
⌃ [0c0d3e7f] PureKLU v1.5.0
  [1fd47b50] QuadGK v2.11.3
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
⌃ [731186ca] RecursiveArrayTools v4.5.1
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.4.0
  [9fe22ead] RespecializeParams v1.3.0
  [79098fc4] Rmath v0.9.0
  [47965b36] RootedTrees v2.27.0
  [f2b01f46] Roots v3.0.8
  [7e49a35a] RuntimeGeneratedFunctions v0.5.26
  [c72e72a9] SDEProblemLibrary v1.2.4
⌃ [0bca4576] SciMLBase v3.54.0
  [31c91b34] SciMLBenchmarks v0.2.1
  [19f34311] SciMLJacobianOperators v0.1.19
  [a6db7da4] SciMLLogging v2.1.0
⌃ [c0aeaf25] SciMLOperators v1.30.0
  [431bcebd] SciMLPublic v1.3.0
  [53ae85a6] SciMLStructures v1.10.5
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [992d4aef] Showoff v1.1.1
  [727e6d20] SimpleNonlinearSolve v2.14.5
  [699a6c99] SimpleTraits v0.9.6
  [a2af1166] SortingAlgorithms v1.2.3
  [a57abbd0] SparseColumnPivotedQR v2.1.8
  [0a514795] SparseMatrixColorings v0.4.28
  [276daf66] SpecialFunctions v2.9.0
  [860ef19b] StableRNGs v1.0.4
⌃ [90137ffa] StaticArrays v1.9.20
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.5
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.13
  [4c63d2b9] StatsFuns v2.2.1
  [789caeaf] StochasticDiffEq v7.2.0
  [19c5a474] StochasticDiffEqCore v2.2.3
  [0520c28c] StochasticDiffEqHighOrder v2.2.0
  [ebf54054] StochasticDiffEqIIF v2.1.0
  [5080b986] StochasticDiffEqImplicit v2.2.1
  [aefaaa88] StochasticDiffEqLeaping v2.1.0
  [90dbc90e] StochasticDiffEqLevyArea v2.1.1
  [d15fe365] StochasticDiffEqLowOrder v2.0.5
  [8c95a807] StochasticDiffEqMilstein v2.1.1
  [db241ea8] StochasticDiffEqROCK v2.1.1
⌃ [49714585] StochasticDiffEqRODE v2.1.0
  [af2a2fcd] StochasticDiffEqWeak v2.2.1
  [69024149] StringEncodings v0.3.7
⌅ [892a3eda] StringManipulation v0.5.0
  [09ab397b] StructArrays v0.7.3
  [2efcf032] SymbolicIndexingInterface v0.3.55
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.14.0
  [62fd8b95] TensorCore v0.1.1
⌃ [a759f4b9] TimerOutputs v1.2.1
  [781d530d] TruncatedStacktraces v1.4.0
  [1cfade01] UnicodeFun v0.4.1
  [41fe7b60] Unzip v0.2.0
  [44d3d7a6] Weave v0.10.12
⌃ [ddb6d928] YAML v0.4.16
  [6e34b625] Bzip2_jll v1.0.9+0
  [83423d85] Cairo_jll v1.18.7+0
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.8.4+0
⌅ [b22a6f82] FFMPEG_jll v8.1.2+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.14.3+1
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.5.1+0
  [d2c73de3] GR_jll v0.73.27+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [7746bdde] Glib_jll v2.88.3+0
  [3b182d85] Graphite2_jll v1.3.16+0
  [2e76f6c2] HarfBuzz_jll v100.14004.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.2.0+1
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.2.0+0
  [1d63c593] LLVMOpenMP_jll v23.1.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.42.0+0
  [89763e89] Libtiff_jll v4.7.3+0
  [38a345b3] Libuuid_jll v2.42.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [458c3c95] OpenSSL_jll v3.5.8+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
  [36c8627f] Pango_jll v1.58.2+0
  [30392449] Pixman_jll v0.46.4+0
  [c0090381] Qt6Base_jll v6.10.2+2
  [629bc702] Qt6Declarative_jll v6.10.2+2
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [f50d1b31] Rmath_jll v0.5.2+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
  [ffd25f8a] XZ_jll v5.8.4+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [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
  [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 v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [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`