ForwardDiff.hessian produces stack overflow for ODEProblem on 3.18

[sebapersson]

Describe the bug 🐞

Starting from 3.18, computing the Hessian for an ODEProblem produces a stack overflow.

Expected behavior

Should be able to compute the gradient.

Minimal Reproducible Example 👇

using OrdinaryDiffEqRosenbrock, ForwardDiff, LinearSolve

function model(du, u, p, t)
    du[1] = p[1] * u[1] - p[2]
end

function my_loss(_p)
    oprob_new = remake(oprob; p = _p)
    sol = solve(oprob_new, Rodas5P(), abstol = 1e-8, reltol = 1e-8)
    return sum(sol)
end

p = [1.0, 2.0]
u0 = [1.0]
oprob = ODEProblem(model, u0, [0.0, 10.0], p)

my_loss(p)
ForwardDiff.hessian(my_loss, p)

Error & Stacktrace ⚠️

Internal error: during type inference of
var"#solve!#106"(LinearSolve.OperatorAssumptions{Nothing}, Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:reltol,), Tuple{Float64}}}, typeof(CommonSolve.solve!), LinearSolve.LinearCache{Array{Float64, 2}, Array{Float64, 1}, Array{Float64, 1}, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, Array{Float64, 2}, Array{Int64, 1}}, LinearAlgebra.QRCompactWY{Float64, Array{Float64, 2}, Array{Float64, 2}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Tuple{LinearAlgebra.LU{Float64, Array{Float64, 2}, Array{Int64, 1}}, Array{Int64, 1}}, Tuple{LinearAlgebra.LU{Float64, Array{Float64, 2}, Array{Int64, 1}}, Array{Int64, 1}}, Nothing, Nothing, Nothing, LinearAlgebra.SVD{Float64, Float64, Array{Float64, 2}, Array{Float64, 1}}, LinearAlgebra.Cholesky{Float64, Array{Float64, 2}}, LinearAlgebra.Cholesky{Float64, Array{Float64, 2}}, Tuple{LinearAlgebra.LU{Float64, Array{Float64, 2}, Array{Int32, 1}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Array{Float64, 2}, Array{Int64, 1}}, Base.RefValue{Int64}}, LinearAlgebra.QRPivoted{Float64, Array{Float64, 2}, Array{Float64, 1}, Array{Int64, 1}}, Nothing, Nothing}, LinearSolve.InvPreconditioner{LinearAlgebra.Diagonal{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, Float64, 2}, 2}, Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, Float64, 2}, 2}, 1}}}, LinearAlgebra.Diagonal{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, Float64, 2}, 2}, Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, ForwardDiff.Dual{ForwardDiff.Tag{typeof(Main.my_loss), Float64}, Float64, 2}, 2}, 1}}, Float64, Bool, LinearSolve.LinearSolveAdjoint{Base.Missing}}, LinearSolve.DefaultLinearSolver, LinearSolve.LUFactorization{LinearAlgebra.RowMaximum}, LinearSolve.LUFactorization{LinearAlgebra.RowMaximum}, LinearSolve.DefaultLinearSolver)
Encountered stack overflow.
This might be caused by recursion over very long tuples or argument lists.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [f6369f11] ForwardDiff v1.0.1
  [7ed4a6bd] LinearSolve v3.18.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.11.0

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

  [47edcb42] ADTypes v1.14.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [4fba245c] ArrayInterface v7.19.0
  [4c555306] ArrayLayouts v1.11.1
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [2a0fbf3d] CPUSummary v0.2.6
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.6.0
  [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 v6.176.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.1
  [ffbed154] DocStringExtensions v0.9.5
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.12
  [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
  [6a86dc24] FiniteDiff v2.27.0
  [f6369f11] ForwardDiff v1.0.1
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [615f187c] IfElse v0.1.1
  [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
  [ba0b0d4f] Krylov v0.10.1
  [b964fa9f] LaTeXStrings v1.4.0
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [7ed4a6bd] LinearSolve v3.18.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [77ba4419] NaNMath v1.1.3
  [bac558e1] OrderedCollections v1.8.1
  [bbf590c4] OrdinaryDiffEqCore v1.26.1
  [4302a76b] OrdinaryDiffEqDifferentiation v1.10.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.11.0
  [d96e819e] Parameters v0.12.3
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.33.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.15
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.102.0
  [c0aeaf25] SciMLOperators v1.3.1
  [53ae85a6] SciMLStructures v1.7.0
  [efcf1570] Setfield v1.1.2
  [ce78b400] SimpleUnPack v1.1.0
  [0a514795] SparseMatrixColorings v0.4.21
  [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
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.1
  [2efcf032] SymbolicIndexingInterface v0.3.41
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [8290d209] ThreadingUtilities v0.5.5
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [856f044c] MKL_jll v2025.0.1+1
  [efe28fd5] OpenSpecFun_jll v0.5.6+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
  [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
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [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 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 14 × Intel(R) Core(TM) Ultra 7 165U
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 14 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1

Additional context

Add any other context about the problem here.

[ChrisRackauckas]

@jClugstor I think this is related to your recent PR, it didn't test nesting of duals.

[jClugstor]

I thought one of the downstream tests covered nested Duals. I think there's one where an ODE problem is defined with dual p, and then is differentiated with Forward diff?

Seems likely that I caused this, but I'm not sure what could be causing a recursion in the type inference...