Describe the bug 🐞
Float64(::ForwardDiff.Dual{..}) error when taking the gradient of a solve for a system with initialization_eqs.
If I remove the initialization_eqs, this seems to work.
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
using ModelingToolkit: t_nounits as t, D_nounits as D
using OrdinaryDiffEqTsit5
using SymbolicIndexingInterface
using ForwardDiff
using SciMLBase: solve, remake, FullSpecialize
using Test
@parameters m=1.5 d=9.0
@variables s(t) v(t)
eqs = [
D(s) ~ v
m * D(v) ~ 1 - d * v
]
sys = mtkcompile(System(eqs, t;
name = :model,
initialization_eqs = [s ~ 0, v ~ 0],
))
prob = ODEProblem{true, FullSpecialize}(sys, [], (0.0, 200.0))
sol = solve(prob, Tsit5(); saveat = 0.1)
@test SciMLBase.successful_retcode(sol)
setter = setp_oop(prob, [sys.m, sys.d])
function loss(x)
p = setter(prob, x)
newprob = remake(prob; p)
newsol = solve(newprob, Tsit5(); saveat = 0.1)
sum(abs2, newsol[sys.s])
end
ForwardDiff.gradient(loss, [3.0, 20.0])Error & Stacktrace ⚠️
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{var"#loss", Float64}, Float64, 2})
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{var"#loss", Float64}, Float64, 2})
@ 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{…}, ::Vector{…}, ::Vector{…}, ::ModelingToolkitBase.MTKParameters{…}, ::Float64)
@ ModelingToolkitBase ./none:0
[6] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Vector{…}, ::Vector{…}, ::ModelingToolkitBase.MTKParameters{…}, ::Float64)
@ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/sqWwp/src/RuntimeGeneratedFunctions.jl:186
[7] _generated_call(::ModelingToolkitBase.GeneratedFunctionWrapper{…}, ::Vector{…}, ::Vector{…}, ::ModelingToolkitBase.MTKParameters{…}, ::Float64)
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/jyweh/src/systems/codegen_utils.jl:417
[8] (::ModelingToolkitBase.GeneratedFunctionWrapper{…})(::Vector{…}, ::Vararg{…})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/jyweh/src/systems/codegen_utils.jl:414
[9] (::SciMLBase.ODEFunction{…})(du::Vector{…}, u::Vector{…}, p::ModelingToolkitBase.MTKParameters{…}, t::Float64)
@ SciMLBase ~/.julia/packages/SciMLBase/Ag5zT/src/scimlfunctions.jl:2662
[10] initialize!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqTsit5.Tsit5Cache{…})
@ OrdinaryDiffEqTsit5 ~/.julia/packages/OrdinaryDiffEqTsit5/8E8fO/src/tsit_perform_step.jl:186
[11] _ode_init(prob::SciMLBase.ODEProblem{…}, alg::OrdinaryDiffEqTsit5.Tsit5{…}, 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::Bool, 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::SciMLBase.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/JWu49/src/solve.jl:47
[12] __init(prob::SciMLBase.ODEProblem{…}, alg::OrdinaryDiffEqTsit5.Tsit5{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}; kwargs::@Kwargs{…})
@ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/JWu49/src/solve.jl:37
[13] __solve(::SciMLBase.ODEProblem{…}, ::OrdinaryDiffEqTsit5.Tsit5{…}; kwargs::@Kwargs{…})
@ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/JWu49/src/solve.jl:9
[14] solve_call(_prob::SciMLBase.ODEProblem{…}, args::OrdinaryDiffEqTsit5.Tsit5{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
@ DiffEqBase ~/.julia/packages/DiffEqBase/ovL8z/src/solve.jl:172
[15] solve_up(prob::SciMLBase.ODEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::ModelingToolkitBase.MTKParameters{…}, args::OrdinaryDiffEqTsit5.Tsit5{…}; originator::SciMLBase.ChainRulesOriginator, kwargs::@Kwargs{…})
@ DiffEqBase ~/.julia/packages/DiffEqBase/ovL8z/src/solve.jl:646
[16] solve(prob::SciMLBase.ODEProblem{…}, args::OrdinaryDiffEqTsit5.Tsit5{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, verbose::Bool, kwargs::@Kwargs{…})
@ DiffEqBase ~/.julia/packages/DiffEqBase/ovL8z/src/solve.jl:591
[17] WARNING: Detected access to binding `Main.loss` in a world prior to its definition world.
Julia 1.12 has introduced more strict world age semantics for global bindings.
!!! This code may malfunction under Revise.
!!! This code will error in future versions of Julia.
Hint: Add an appropriate `invokelatest` around the access to this binding.
To make this warning an error, and hence obtain a stack trace, use `julia --depwarn=error`.
loss(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#loss", Float64}, Float64, 2}})
@ Main ~/work/dev/upstream_bugs/mtk_forwarddiff_iip/initialization_eqs.jl:31
[18] vector_mode_dual_eval!
@ ~/.julia/packages/ForwardDiff/z3jRk/src/apiutils.jl:24 [inlined]
[19] vector_mode_gradient(f::var"#loss", x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
@ ForwardDiff ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:98
[20] gradient
@ ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:20 [inlined]
[21] gradient(f::var"#loss", x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{…}, Float64, 2, Vector{…}})
@ ForwardDiff ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:17
[22] gradient(f::var"#loss", x::Vector{Float64})
@ ForwardDiff ~/.julia/packages/ForwardDiff/z3jRk/src/gradient.jl:17
[23] top-level scope
@ ~/work/dev/upstream_bugs/mtk_forwarddiff_iip/initialization_eqs.jl:35
Some type information was truncated. Use `show(err)` to see complete types.Environment (please complete the following information):
- Output of
using Pkg; Pkg.status()
[f6369f11] ForwardDiff v1.3.3
[5903a43b] Infiltrator v1.9.10
[961ee093] ModelingToolkit v11.21.0
[7771a370] ModelingToolkitBase v1.30.0
[6bb917b9] ModelingToolkitTearing v1.12.3
[43230ef6] OrdinaryDiffEqRosenbrock v1.31.0
[b1df2697] OrdinaryDiffEqTsit5 v1.12.0
⌅ [0bca4576] SciMLBase v2.155.0
[2efcf032] SymbolicIndexingInterface v0.3.46
- Output of
using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
[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 v7.24.0
[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 v6.217.0
[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 v2.30.0
[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 v1.11.0
[313cdc1a] Indexing v1.1.1
[5903a43b] Infiltrator v1.9.10
[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
[961ee093] ModelingToolkit v11.21.0
[7771a370] ModelingToolkitBase v1.30.0
[6bb917b9] ModelingToolkitTearing v1.12.3
[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 v3.32.0
[4302a76b] OrdinaryDiffEqDifferentiation v2.9.0
[43230ef6] OrdinaryDiffEqRosenbrock v1.31.0
[b1df2697] OrdinaryDiffEqTsit5 v1.12.0
[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 v1.13.0
[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 v0.4.27
[276daf66] SpecialFunctions v2.7.2
[0c0c59c1] StarAlgebras v0.3.0
[64909d44] StateSelection v1.9.1
[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 v4.24.2
[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
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.
Describe the bug 🐞
Float64(::ForwardDiff.Dual{..})error when taking the gradient of asolvefor a system withinitialization_eqs.If I remove the
initialization_eqs, this seems to work.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.
Error & Stacktrace⚠️
Environment (please complete the following information):
using Pkg; Pkg.status()using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)versioninfo()Additional context
Add any other context about the problem here.