`Float64(::ForwardDiff.Dual{..})` error when differentiating over SCCNonlinearProblem

[SebastianM-C]

Describe the bug 🐞

Using ForwardDiff.gradient over a DAE with SCCNonlinearProblem in initialization leads to a Float64(::ForwardDiff.Dual{..}) error.

Expected behavior

No error.

Minimal Reproducible Example 👇

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, OrdinaryDiffEqRosenbrock, ForwardDiff, SciMLBase
using ModelingToolkit: t_nounits as t, D_nounits as D
const MTKBase = ModelingToolkit.ModelingToolkitBase
using SymbolicIndexingInterface
using Test

@parameters L = 1. g = 1.

@variables x(t) y(t) [state_priority = 10] λ(t)
eqs = [D(D(x)) ~ λ * x
    D(D(y)) ~ λ * y - g
    x^2 + y^2 ~ L^2]
@mtkcompile pend = System(eqs, t)
model = mtkcompile(System(eqs, t; name = :pendulum))

g_true = 9.81
prob = ODEProblem(pend, [x => 1, D(y) => 0, g=>g_true], (0.0, 0.5);
    guesses = [λ => 0, y => 1, x => 1])
saveat = range(prob.tspan..., length = 30)
sol = solve(prob, Rodas5P(); saveat)
@test SciMLBase.successful_retcode(sol)

setter = setp_oop(prob, [g])

function costfn(theta)
   p = setter(prob, theta)
   newprob = SciMLBase.remake(prob; p)
   sol = solve(newprob, Rodas5P(); saveat=0.1)
   sum(abs2, sol[x])
end

@test costfn([1.2]) ≠ zeros(1)
@test ForwardDiff.gradient(costfn, [1.2]) ≠ zeros(1)

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(costfn), Float64}, Float64, 1})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:965
  Float64(::IrrationalConstants.Sqrt2π)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/RokwY/src/macro.jl:111
  ...

Stacktrace:
  [1] convert(::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(costfn), Float64}, Float64, 1})
    @ Base ./number.jl:7
  [2] setindex!
    @ ./array.jl:985 [inlined]
  [3] macro expansion
    @ ~/.julia/packages/RuntimeGeneratedFunctions/sqWwp/src/RuntimeGeneratedFunctions.jl:200 [inlined]
  [4] macro expansion
    @ ./none:0 [inlined]
  [5] generated_callfunc(::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…}, ::Tuple{…}, ::Tuple{}, ::MTKParameters{…})
    @ ModelingToolkitBase ./none:0
  [6] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Tuple{…}, ::Tuple{}, ::MTKParameters{…})
    @ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/sqWwp/src/RuntimeGeneratedFunctions.jl:186
  [7] _generated_call(::ModelingToolkitBase.GeneratedFunctionWrapper{…}, ::Tuple{…}, ::Tuple{}, ::MTKParameters{…})
    @ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/jyweh/src/systems/codegen_utils.jl:417
  [8] (::ModelingToolkitBase.GeneratedFunctionWrapper{…})(::Tuple{…}, ::Vararg{…})
    @ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/jyweh/src/systems/codegen_utils.jl:414
  [9] (::ModelingToolkit.CacheWriter{…})(p::MTKParameters{…}, sols::Tuple{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/wVorF/src/problems/sccnonlinearproblem.jl:6
 [10] solve_single_scc(alg::SCCNonlinearSolve.SCCAlg{…}, prob::NonlinearProblem{…}, explicitfun::ModelingToolkit.CacheWriter{…}, sols::Tuple{}; kwargs::@Kwargs{…})
    @ SCCNonlinearSolve ~/.julia/packages/SCCNonlinearSolve/NOZYN/src/SCCNonlinearSolve.jl:77
 [11] macro expansion
    @ ~/.julia/packages/SCCNonlinearSolve/NOZYN/src/SCCNonlinearSolve.jl:127 [inlined]
 [12] iteratively_build_sols(alg::SCCNonlinearSolve.SCCAlg{…}, probs::Tuple{…}, explicitfuns::Tuple{…}, ::Val{…}; kwargs::@Kwargs{…})
    @ SCCNonlinearSolve ~/.julia/packages/SCCNonlinearSolve/NOZYN/src/SCCNonlinearSolve.jl:124
 [13] _scc_solve(prob::SCCNonlinearProblem{…}, alg::SCCNonlinearSolve.SCCAlg{…}; kwargs::@Kwargs{…})
    @ SCCNonlinearSolve ~/.julia/packages/SCCNonlinearSolve/NOZYN/src/SCCNonlinearSolve.jl:169
 [14] scc_solve_up(prob::SCCNonlinearProblem{…}, sensealg::Nothing, u0::Nothing, p::MTKParameters{…}, alg::SCCNonlinearSolve.SCCAlg{…}; kwargs::@Kwargs{…})
    @ SCCNonlinearSolve ~/.julia/packages/SCCNonlinearSolve/NOZYN/src/SCCNonlinearSolve.jl:69
 [15] solve(prob::SCCNonlinearProblem{…}, alg::SCCNonlinearSolve.SCCAlg{…}; sensealg::Nothing, u0::Nothing, p::Nothing, kwargs::@Kwargs{…})
    @ SCCNonlinearSolve ~/.julia/packages/SCCNonlinearSolve/NOZYN/src/SCCNonlinearSolve.jl:52
 [16] solve(prob::SCCNonlinearProblem{…}, alg::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; sensealg::Nothing, u0::Nothing, p::Nothing, kwargs::@Kwargs{…})
    @ SCCNonlinearSolve ~/.julia/packages/SCCNonlinearSolve/NOZYN/src/SCCNonlinearSolve.jl:49
 [17] get_initial_values(prob::ODEProblem{…}, valp::OrdinaryDiffEqCore.ODEIntegrator{…}, f::ODEFunction{…}, alg::SciMLBase.OverrideInit{…}, iip::Val{…}; nlsolve_alg::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}, abstol::Float64, reltol::Float64, kwargs::@Kwargs{})
    @ SciMLBase ~/.julia/packages/SciMLBase/Ag5zT/src/initialization.jl:308
 [18] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::SciMLBase.OverrideInit{…}, isinplace::Val{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/initialize_dae.jl:137
 [19] _initialize_dae!
    @ ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/initialize_dae.jl:34 [inlined]
 [20] initialize_dae! (repeats 2 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/initialize_dae.jl:20 [inlined]
 [21] _ode_init(prob::ODEProblem{…}, alg::Rodas5P{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}; saveat::Float64, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_discretes::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Nothing, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, abstol::Nothing, reltol::Nothing, gamma::Nothing, qmin::Nothing, qmax::Nothing, qsteady_min::Nothing, qsteady_max::Nothing, beta1::Nothing, beta2::Nothing, qoldinit::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::Standard, controller::Nothing, 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::DiffEqBase.DefaultInit, rng::Nothing, save_noise::Bool, delta::Nothing, W::Nothing, P::Nothing, sqdt::Nothing, noise::Nothing, c::Nothing, rate_constants::Nothing, _cache::Nothing, _u::Nothing, _uprev::Nothing, seed::UInt64, kwargs::@Kwargs{})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/solve.jl:784
 [22] _ode_init
    @ ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/solve.jl:47 [inlined]
 [23] #__init#60
    @ ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/solve.jl:37 [inlined]
 [24] __init (repeats 2 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/solve.jl:19 [inlined]
 [25] #__solve#59
    @ ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/solve.jl:9 [inlined]
 [26] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/bDZEh/src/solve.jl:1 [inlined]
 [27] #solve_call#22
    @ ~/.julia/packages/DiffEqBase/3Bxly/src/solve.jl:172 [inlined]
 [28] solve_up(prob::ODEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::MTKParameters{…}, args::Rodas5P{…}; originator::SciMLBase.ChainRulesOriginator, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3Bxly/src/solve.jl:646
 [29] solve(prob::ODEProblem{…}, args::Rodas5P{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3Bxly/src/solve.jl:591
 [30] costfn(theta::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(costfn), Float64}, Float64, 1}})
    @ Main ~/work/dev/upstream_bugs/mtk_forwarddiff_iip/scc.jl:28
 [31] vector_mode_dual_eval!
    @ ~/.julia/packages/ForwardDiff/z3jRk/src/apiutils.jl:24 [inlined]
 [32] vector_mode_gradient(f::typeof(costfn), x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:98
 [33] gradient
    @ ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:20 [inlined]
 [34] gradient(f::typeof(costfn), x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:17
 [35] gradient(f::typeof(costfn), x::Vector{Float64})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:17

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `/tmp/jl_MMaivz/Project.toml`
  [f6369f11] ForwardDiff v1.3.3
  [7771a370] ModelingToolkitBase v1.30.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.31.0
  [2efcf032] SymbolicIndexingInterface v0.3.46
  [d1185830] SymbolicUtils v4.24.1
  [0c5d862f] Symbolics v7.18.1
  [8dfed614] Test v1.11.0

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `/tmp/jl_MMaivz/Manifest.toml`
  [47edcb42] ADTypes v1.21.0
  [6e696c72] AbstractPlutoDingetjes v1.3.2
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.44
  [79e6a3ab] Adapt v4.5.2
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.23.0
  [4c555306] ArrayLayouts v1.12.2
  [aae01518] BandedMatrices v1.11.0
  [e2ed5e7c] Bijections v0.2.2
  [caf10ac8] BipartiteGraphs v0.1.7
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.9.3
  [70df07ce] BracketingNonlinearSolve v1.12.1
  [2a0fbf3d] CPUSummary v0.2.7
  [fb6a15b2] CloseOpenIntervals v0.1.13
⌅ [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.6
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.18.1
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.6.0
  [adafc99b] CpuId v0.3.1
  [864edb3b] DataStructures v0.19.4
  [85a47980] Dictionaries v0.4.6
  [2b5f629d] DiffEqBase v6.216.0
  [459566f4] DiffEqCallbacks v4.14.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.16
  [ffbed154] DocStringExtensions v0.9.5
⌅ [5b8099bc] DomainSets v0.7.18
  [7c1d4256] DynamicPolynomials v0.6.6
  [4e289a0a] EnumX v1.0.7
  [f151be2c] EnzymeCore v0.8.19
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [7034ab61] FastBroadcast v1.3.1
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.3.1
  [1a297f60] FillArrays v1.16.0
  [64ca27bc] FindFirstFunctions v1.8.0
  [6a86dc24] FiniteDiff v2.29.0
  [f6369f11] ForwardDiff v1.3.3
  [a85aefff] FunctionMaps v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v1.4.0
  [46192b85] GPUArraysCore v0.2.0
  [86223c79] Graphs v1.14.0
  [615f187c] IfElse v0.1.1
  [3263718b] ImplicitDiscreteSolve v1.10.0
  [313cdc1a] Indexing v1.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.3
  [8197267c] IntervalSets v0.7.14
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.1
  [ae98c720] Jieko v0.2.1
  [ccbc3e58] JumpProcesses v9.25.1
  [ba0b0d4f] Krylov v0.10.6
  [10f19ff3] LayoutPointers v0.1.17
  [87fe0de2] LineSearch v0.1.7
  [7ed4a6bd] LinearSolve v3.75.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [7771a370] ModelingToolkitBase v1.30.0
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.18
  [d8a4904e] MutableArithmetics v1.7.1
  [77ba4419] NaNMath v1.1.3
  [be0214bd] NonlinearSolveBase v2.24.0
  [5959db7a] NonlinearSolveFirstOrder v2.1.1
  [6fe1bfb0] OffsetArrays v1.17.0
  [bac558e1] OrderedCollections v1.8.1
  [bbf590c4] OrdinaryDiffEqCore v3.31.0
  [4302a76b] OrdinaryDiffEqDifferentiation v2.9.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.31.0
  [e409e4f3] PoissonRandom v0.4.7
  [f517fe37] Polyester v0.7.19
  [1d0040c9] PolyesterWeave v0.2.2
  [d236fae5] PreallocationTools v1.2.0
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.2
  [27ebfcd6] Primes v0.5.7
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
  [3cdcf5f2] RecipesBase v1.3.4
⌅ [731186ca] RecursiveArrayTools v3.54.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.18
  [9dfe8606] SCCNonlinearSolve v1.12.1
  [94e857df] SIMDTypes v0.1.0
⌅ [0bca4576] SciMLBase v2.155.0
  [19f34311] SciMLJacobianOperators v0.1.13
  [a6db7da4] SciMLLogging v1.9.1
  [c0aeaf25] SciMLOperators v1.16.0
  [431bcebd] SciMLPublic v1.0.1
  [53ae85a6] SciMLStructures v1.10.0
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.11.1
  [699a6c99] SimpleTraits v0.9.5
  [0a514795] SparseMatrixColorings v0.4.26
  [276daf66] SpecialFunctions v2.7.2
  [0c0c59c1] StarAlgebras v0.3.0
  [aedffcd0] Static v1.3.1
  [0d7ed370] StaticArrayInterface v1.9.0
  [90137ffa] StaticArrays v1.9.18
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [7792a7ef] StrideArraysCore v0.5.8
  [2efcf032] SymbolicIndexingInterface v0.3.46
  [19f23fe9] SymbolicLimits v1.1.0
  [d1185830] SymbolicUtils v4.24.1
  [0c5d862f] Symbolics v7.18.1
  [ed4db957] TaskLocalValues v0.1.3
  [8ea1fca8] TermInterface v2.0.0
  [8290d209] ThreadingUtilities v0.5.5
  [a759f4b9] TimerOutputs v0.5.29
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [d30d5f5c] WeakCacheSets v0.1.0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
  [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
  [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
  [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
  [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 ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × Intel(R) Core(TM) i9-14900K
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, alderlake)
  GC: Built with stock GC
Threads: 32 default, 1 interactive, 32 GC (on 32 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1

Additional context

Add any other context about the problem here.