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ERROR: BoundsError: attempt to access 0-element Vector{ForwardDiff.Dual{...} at index [1] when using ForwardDiff with a DAEΒ #3634

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ERROR: BoundsError: attempt to access 0-element Vector{ForwardDiff.Dual{...} at index [1] when using ForwardDiff with a DAE#3634
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bugSomething isn't working
@SebastianM-C

Description

@SebastianM-C
SebastianM-C
opened on May 14, 2025

Describe the bug 🐞

I'm seeing a bounds error from inside initialization when trying to differentiate a DAE solve with ForwardDiff.

The MWE below is not super minimal because of the MTKNN dependency, but I'm not yet able to get a MWE on a simpler system. I'll try to simplify this more and update the issue.

Expected behavior

No errors.

Minimal Reproducible Example πŸ‘‡

Without MRE, we would only be able to help you to a limited extent, and attention to the issue would be limited. to know more about MRE refer to wikipedia and stackoverflow.

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using OrdinaryDiffEqRosenbrock, OrdinaryDiffEqNonlinearSolve
using SymbolicIndexingInterface
using SciMLBase
using DifferentiationInterface
using ModelingToolkitNeuralNets, Lux
using ModelingToolkitStandardLibrary.Blocks
using ModelingToolkitStandardLibrary.Thermal

@mtkmodel ThermalNN begin
    begin
        n_input = 3
        n_output = 2
        chain = Lux.Chain(
            Lux.Dense(n_input => 4, Lux.mish, use_bias=false),
            Lux.Dense(4 => 4, Lux.mish, use_bias=false),
            Lux.Dense(4 => n_output, use_bias=false)
        )
    end
    @components begin
        port_a = HeatPort()
        port_b = HeatPort()
        nn = NeuralNetworkBlock(; n_input, n_output, chain)
    end
    @variables begin
        dT(t), [guess = 0.0]
        Q_flow(t), [guess = 0.0]
        x(t) = 273.15
    end
    @equations begin
        dT ~ port_a.T - port_b.T
        port_a.Q_flow ~ Q_flow
        D(x) ~ nn.output.u[1]
        Q_flow ~ nn.output.u[1]
        port_b.Q_flow ~ nn.output.u[1] + nn.output.u[2]
        nn.input.u[1] ~ (x - 273.15) / 30
        nn.input.u[2] ~ (port_a.T - 273.15) / 30
        nn.input.u[3] ~ (port_b.T - 273.15) / 30
    end
end

@mtkmodel NeuralPot begin
    @parameters begin
        C2 = 15
    end
    @components begin
        input = Blocks.Constant(k=1)
        source = PrescribedHeatFlow(T_ref=273.15)
        pot = HeatCapacitor(C=C2, T=273.15)
        air = ThermalConductor(G=0.1)
        env = FixedTemperature(T=293.15)
        Tsensor = TemperatureSensor()
        nn = ThermalNN()
    end
    @equations begin
        connect(input.output, :u, source.Q_flow)
        connect(pot.port, Tsensor.port)
        connect(pot.port, air.port_a)
        connect(air.port_b, env.port)
        connect(source.port, nn.port_a)
        connect(nn.port_b, pot.port)
    end
end

@mtkbuild sys = NeuralPot()

prob = ODEProblem(sys, [], (0., 100), [])

tp = [Initial(sys.nn.x)]
x0 = [273]

oop_update = setsym_oop(prob, tp);

get_vars = getsym(prob, [sys.pot.T]);

function loss(x, (prob, ts, setter, get_vars))
    (u0, p) = setter(prob, x)
    new_prob = remake(prob; u0, p)

    new_sol = solve(new_prob, Rodas5P(); saveat=ts)

    u = get_vars(new_sol)

    !SciMLBase.successful_retcode(new_sol) && return Inf

    sum(u)
end

ts = collect(0:100);
ps = (prob, ts, oop_update, get_vars);

loss(x0, ps)

DifferentiationInterface.gradient(x -> loss(x, ps), AutoForwardDiff(), x0)

Error & Stacktrace ⚠️

ERROR: BoundsError: attempt to access 0-element Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#13#14", Int64}, Float64, 1}} at index [1]
Stacktrace:
  [1] throw_boundserror(A::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#13#14", Int64}, Float64, 1}}, I::Tuple{Int64})
    @ Base ./essentials.jl:14
  [2] getindex
    @ ./essentials.jl:916 [inlined]
  [3] getindex
    @ ~/.julia/packages/StaticArrays/LSPcF/src/SizedArray.jl:92 [inlined]
  [4] macro expansion
    @ ~/.julia/packages/SymbolicUtils/0GKgW/src/code.jl:510 [inlined]
  [5] macro expansion
    @ ~/.julia/packages/Symbolics/kQzvO/src/build_function.jl:368 [inlined]
  [6] macro expansion
    @ ~/.julia/packages/RuntimeGeneratedFunctions/RrXEW/src/RuntimeGeneratedFunctions.jl:161 [inlined]
  [7] macro expansion
    @ ./none:0 [inlined]
  [8] generated_callfunc
    @ ./none:0 [inlined]
  [9] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Vector{…}, ::Vector{…}, ::MTKParameters{…})
    @ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/RrXEW/src/RuntimeGeneratedFunctions.jl:148
 [10] macro expansion
    @ ~/.julia/packages/ModelingToolkit/q2akl/src/systems/codegen_utils.jl:0 [inlined]
 [11] _generated_call(::ModelingToolkit.GeneratedFunctionWrapper{…}, ::Vector{…}, ::Vector{…}, ::MTKParameters{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/q2akl/src/systems/codegen_utils.jl:262
 [12] (::ModelingToolkit.GeneratedFunctionWrapper{…})(::Vector{…}, ::Vararg{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/q2akl/src/systems/codegen_utils.jl:259
 [13] (::NonlinearFunction{…})(::Vector{…}, ::Vararg{…})
    @ SciMLBase ~/.julia/packages/SciMLBase/JKXkh/src/scimlfunctions.jl:2574
 [14] evaluate_f(prob::NonlinearProblem{…}, u::Vector{…})
    @ NonlinearSolveBase.Utils ~/.julia/packages/NonlinearSolveBase/vY49C/src/utils.jl:174
 [15] __init(::NonlinearProblem{…}, ::NonlinearSolveQuasiNewton.QuasiNewtonAlgorithm{…}; stats::SciMLBase.NLStats, alias_u0::Bool, maxtime::Nothing, maxiters::Int64, abstol::Float64, reltol::Float64, linsolve_kwargs::@NamedTuple{}, termination_condition::Nothing, internalnorm::typeof(NonlinearSolveBase.L2_NORM), initializealg::NonlinearSolveBase.NonlinearSolveDefaultInit, kwargs::@Kwargs{…})
    @ NonlinearSolveQuasiNewton ~/.julia/packages/NonlinearSolveQuasiNewton/YURnD/src/solve.jl:149
 [16] __solve(::NonlinearProblem{…}, ::NonlinearSolveQuasiNewton.QuasiNewtonAlgorithm{…}; kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/vY49C/src/solve.jl:5
 [17] macro expansion
    @ ~/.julia/packages/NonlinearSolveBase/vY49C/src/solve.jl:173 [inlined]
 [18] __generated_polysolve(::NonlinearProblem{…}, ::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; stats::SciMLBase.NLStats, alias_u0::Bool, verbose::Bool, initializealg::NonlinearSolveBase.NonlinearSolveDefaultInit, kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/vY49C/src/solve.jl:130
 [19] __solve(::NonlinearProblem{…}, ::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/vY49C/src/solve.jl:127
 [20] solve_call(_prob::NonlinearProblem{…}, args::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:667
 [21] solve_up(prob::NonlinearProblem{…}, sensealg::Nothing, u0::Vector{…}, p::MTKParameters{…}, args::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1183
 [22] solve(prob::NonlinearProblem{…}, args::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1171
 [23] get_initial_values(prob::ODEProblem{…}, valp::OrdinaryDiffEqCore.ODEIntegrator{…}, f::Function, alg::SciMLBase.OverrideInit{…}, iip::Val{…}; nlsolve_alg::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}, abstol::Float64, reltol::Float64, kwargs::@Kwargs{})
    @ SciMLBase ~/.julia/packages/SciMLBase/JKXkh/src/initialization.jl:284
 [24] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::SciMLBase.OverrideInit{…}, isinplace::Val{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/initialize_dae.jl:151
 [25] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::OrdinaryDiffEqCore.DefaultInit, x::Val{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/initialize_dae.jl:50
 [26] initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, initializealg::OrdinaryDiffEqCore.DefaultInit)
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/initialize_dae.jl:40
 [27] __init(prob::ODEProblem{…}, alg::Rodas5P{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{…}; saveat::Vector{…}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{…}, abstol::Nothing, reltol::Nothing, qmin::Rational{…}, qmax::Int64, qsteady_min::Int64, qsteady_max::Rational{…}, beta1::Nothing, beta2::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias::ODEAliasSpecifier, initializealg::OrdinaryDiffEqCore.DefaultInit, kwargs::@Kwargs{})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:565
 [28] __init (repeats 5 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:11 [inlined]
 [29] __solve(::ODEProblem{…}, ::Rodas5P{…}; kwargs::@Kwargs{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:6
 [30] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:1 [inlined]
 [31] #solve_call#36
    @ ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:667 [inlined]
 [32] solve_up(prob::ODEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::MTKParameters{…}, args::Rodas5P{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1199
 [33] solve_up
    @ ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1177 [inlined]
 [34] solve(prob::ODEProblem{…}, args::Rodas5P{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1089
 [35] loss(x::Vector{…}, ::Tuple{…})
    @ Main ~/juliasim/dev/dae_ad.jl:215
 [36] (::var"#13#14")(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#13#14", Int64}, Int64, 1}})
    @ Main ~/juliasim/dev/dae_ad.jl:229
 [37] vector_mode_dual_eval!
    @ ~/.julia/packages/ForwardDiff/UBbGT/src/apiutils.jl:24 [inlined]
 [38] vector_mode_gradient(f::var"#13#14", x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:91
 [39] gradient
    @ ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:20 [inlined]
 [40] gradient(f::var"#13#14", x::Vector{Int64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{…}, Int64, 1, Vector{…}})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:17
 [41] gradient(f::var"#13#14", x::Vector{Int64})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:17
 [42] gradient(::var"#13#14", ::AutoForwardDiff{nothing, Nothing}, ::Vector{Int64})
    @ DifferentiationInterfaceForwardDiffExt ~/.julia/packages/DifferentiationInterface/zJHX8/ext/DifferentiationInterfaceForwardDiffExt/onearg.jl:350
 [43] top-level scope
    @ ~/dev/dae_ad.jl:229
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

  • Output of using Pkg; Pkg.status()
(jl_mF94wp) pkg> st
Status `/tmp/jl_mF94wp/Project.toml`
βŒ… [a0c0ee7d] DifferentiationInterface v0.6.54
  [b2108857] Lux v1.12.4
  [961ee093] ModelingToolkit v9.79.0
  [f162e290] ModelingToolkitNeuralNets v1.7.0
  [16a59e39] ModelingToolkitStandardLibrary v2.21.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.8.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.10.0
  [0bca4576] SciMLBase v2.89.1
  [2efcf032] SymbolicIndexingInterface v0.3.40
  • Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
(jl_mF94wp) pkg> st -m
Status `/tmp/jl_mF94wp/Manifest.toml`
  [47edcb42] ADTypes v1.14.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.5.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.19.0
  [4c555306] ArrayLayouts v1.11.1
  [a9b6321e] Atomix v1.1.1
  [e2ed5e7c] Bijections v0.1.10
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.6.3
  [70df07ce] BracketingNonlinearSolve v1.2.0
  [2a0fbf3d] CPUSummary v0.2.6
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [861a8166] Combinatorics v1.0.3
  [a80b9123] CommonMark v0.9.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b0b7db55] ComponentArrays v0.15.27
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.8
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.173.0
  [459566f4] DiffEqCallbacks v4.5.0
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
βŒ… [a0c0ee7d] DifferentiationInterface v0.6.54
  [8d63f2c5] DispatchDoctor v0.4.19
  [31c24e10] Distributions v0.25.120
  [ffbed154] DocStringExtensions v0.9.4
  [5b8099bc] DomainSets v0.7.15
  [7c1d4256] DynamicPolynomials v0.6.1
  [06fc5a27] DynamicQuantities v1.8.0
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.8
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.1.2
  [1a297f60] FillArrays v1.13.0
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.27.0
  [1fa38f19] Format v1.3.7
βŒ… [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [46192b85] GPUArraysCore v0.2.0
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.1
  [076d061b] HashArrayMappedTries v0.2.0
  [34004b35] HypergeometricFunctions v0.3.28
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.11
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.0
  [ae98c720] Jieko v0.2.1
  [98e50ef6] JuliaFormatter v2.1.2
βŒ… [70703baa] JuliaSyntax v0.4.10
  [ccbc3e58] JumpProcesses v9.14.3
  [63c18a36] KernelAbstractions v0.9.34
  [ba0b0d4f] Krylov v0.10.1
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.7
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v3.12.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [b2108857] Lux v1.12.4
  [bb33d45b] LuxCore v1.2.4
  [82251201] LuxLib v1.7.3
  [7e8f7934] MLDataDevices v1.9.1
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.79.0
  [f162e290] ModelingToolkitNeuralNets v1.7.0
  [16a59e39] ModelingToolkitStandardLibrary v2.21.1
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.9
  [d8a4904e] MutableArithmetics v1.6.4
  [d41bc354] NLSolversBase v7.9.1
  [872c559c] NNlib v0.9.30
  [77ba4419] NaNMath v1.1.3
  [8913a72c] NonlinearSolve v4.8.0
  [be0214bd] NonlinearSolveBase v1.9.0
  [5959db7a] NonlinearSolveFirstOrder v1.5.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.5.0
  [26075421] NonlinearSolveSpectralMethods v1.2.0
  [6fe1bfb0] OffsetArrays v1.17.0
  [429524aa] Optim v1.12.0
  [3bd65402] Optimisers v0.4.6
  [bac558e1] OrderedCollections v1.8.0
  [bbf590c4] OrdinaryDiffEqCore v1.25.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.8.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.8.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.10.0
  [90014a1f] PDMats v0.11.35
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.27
βŒ… [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.7
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.33.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.14
  [9dfe8606] SCCNonlinearSolve v1.2.0
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.89.1
  [19f34311] SciMLJacobianOperators v0.1.5
  [c0aeaf25] SciMLOperators v0.4.0
  [53ae85a6] SciMLStructures v1.7.0
  [7e506255] ScopedValues v1.3.0
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.5.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [0a514795] SparseMatrixColorings v0.4.19
  [276daf66] SpecialFunctions v2.5.1
  [aedffcd0] Static v1.2.0
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.13
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.5
  [4c63d2b9] StatsFuns v1.5.0
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.1
  [2efcf032] SymbolicIndexingInterface v0.3.40
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.27.0
  [0c5d862f] Symbolics v6.39.1
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [ed4db957] TaskLocalValues v0.1.2
  [8ea1fca8] TermInterface v2.0.0
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.3
  [a759f4b9] TimerOutputs v0.5.28
  [410a4b4d] Tricks v0.1.10
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.2
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.22.1
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.3.0
  [897b6980] WeakValueDicts v0.1.0
  [d49dbf32] WeightInitializers v1.1.1
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [856f044c] MKL_jll v2025.0.1+1
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [f50d1b31] Rmath_jll v0.5.1+0
  [1317d2d5] oneTBB_jll v2022.0.0+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
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays 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
  [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
  • Output of versioninfo()
Julia Version 1.11.5
Commit 2d89891cf85 (2025-04-22 21:22 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 Γ— Intel(R) Core(TM) i9-14900K
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 32 default, 0 interactive, 16 GC (on 32 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1

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