SplitODEProblem doesn't work with ForwardDiff in in-place mode.

[ctessum]

Describe the bug 🐞

I would like to use ForwardDiff to calculate the sensitivity of an ODE system using a split problem. It currently works with an out-of-place ODE function, but it doesn't work with an in-place function.

Expected behavior

I would expect it to work both in place and out-of-place.

Minimal Reproducible Example 👇

using DifferentialEquations
using ForwardDiff
using LinearAlgebra
using SciMLSensitivity
using Test

f1(du, u, p, t) = du .= -p
f1(u, p, t) = -p

f2(du, u, p, t) = du .= 2p
f2(u, p, t) = 2p

p = rand(3)
prob = SplitODEProblem{false}(f1, f2, zeros(3), (0, 1), p)
sol = solve(prob)
@test sol[end] ≈ p # 0 - p + 2p = p

function loss(p)
    u0 = Vector{eltype(p)}(prob.u0)
    _prob = remake(prob, u0=u0, p=p)
    sol = solve(_prob)
    norm(sol[end])
end

ForwardDiff.gradient(loss, p) # Works with out-of-place problem

prob = SplitODEProblem{true}(f1, f2, zeros(3), (0, 1), p)

ForwardDiff.gradient(loss, p) # Does not work with in-place problem

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(loss), Float64}, Float64, 3})
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:900
  Float64(::Int16)
   @ Base float.jl:239
  ...

Stacktrace:
  [1] convert(::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(loss), Float64}, Float64, 3})
    @ Base ./number.jl:7
  [2] setindex!(A::Memory{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(loss), Float64}, Float64, 3}, i1::Int64)
    @ Base ./genericmemory.jl:243
  [3] unsafe_copyto!(dest::Memory{Float64}, doffs::Int64, src::Memory{ForwardDiff.Dual{…}}, soffs::Int64, n::Int64)
    @ Base ./genericmemory.jl:153
  [4] unsafe_copyto!
    @ ./genericmemory.jl:133 [inlined]
  [5] _copyto_impl!
    @ ./array.jl:308 [inlined]
  [6] copyto!
    @ ./array.jl:294 [inlined]
  [7] copyto!
    @ ./array.jl:319 [inlined]
  [8] copyto!
    @ ./broadcast.jl:961 [inlined]
  [9] copyto!
    @ ./broadcast.jl:920 [inlined]
 [10] materialize!
    @ ./broadcast.jl:878 [inlined]
 [11] materialize!
    @ ./broadcast.jl:875 [inlined]
 [12] f1(du::Vector{Float64}, u::Vector{ForwardDiff.Dual{…}}, p::Vector{ForwardDiff.Dual{…}}, t::Float64)
    @ Main ~/...:10
 [13] ODEFunction
    @ ~/.julia/packages/SciMLBase/YTOjh/src/scimlfunctions.jl:2468 [inlined]
 [14] (::SplitFunction{…})(du::Vector{…}, u::Vector{…}, p::Vector{…}, t::Float64)
    @ SciMLBase ~/.julia/packages/SciMLBase/YTOjh/src/scimlfunctions.jl:2485
 [15] initialize!
    @ ~/.julia/packages/OrdinaryDiffEqTsit5/DHYtz/src/tsit_perform_step.jl:175 [inlined]
 [16] initialize!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqCore.DefaultCache{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/yTEch/src/perform_step/composite_perform_step.jl:38
 [17] __init(prob::ODEProblem{…}, alg::CompositeAlgorithm{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{…}; saveat::Tuple{}, 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::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(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/yTEch/src/solve.jl:587
 [18] __init (repeats 5 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/yTEch/src/solve.jl:11 [inlined]
 [19] #__solve#62
    @ ~/.julia/packages/OrdinaryDiffEqCore/yTEch/src/solve.jl:6 [inlined]
 [20] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/yTEch/src/solve.jl:1 [inlined]
 [21] solve_call(_prob::ODEProblem{…}, args::CompositeAlgorithm{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:635
 [22] solve_call
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:592 [inlined]
 [23] #solve_up#44
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1124 [inlined]
 [24] solve_up
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1102 [inlined]
 [25] #solve#42
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1041 [inlined]
 [26] solve
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1029 [inlined]
 [27] #__solve#3
    @ ~/.julia/packages/OrdinaryDiffEqDefault/kOV75/src/default_alg.jl:48 [inlined]
 [28] __solve
    @ ~/.julia/packages/OrdinaryDiffEqDefault/kOV75/src/default_alg.jl:47 [inlined]
 [29] #__solve#63
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1432 [inlined]
 [30] __solve
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1423 [inlined]
 [31] #solve_call#35
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:635 [inlined]
 [32] solve_call(::ODEProblem{Vector{…}, Tuple{…}, true, Vector{…}, SplitFunction{…}, @Kwargs{}, SplitODEProblem{…}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:592
 [33] solve_up(::ODEProblem{…}, ::Nothing, ::Vector{…}, ::Vector{…}; kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1108
 [34] solve_up
    @ ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1102 [inlined]
 [35] solve(::ODEProblem{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1039
 [36] solve(::ODEProblem{Vector{…}, Tuple{…}, true, Vector{…}, SplitFunction{…}, @Kwargs{}, SplitODEProblem{…}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/l2ROR/src/solve.jl:1029
 [37] loss(p::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(loss), Float64}, Float64, 3}})
    @ Main ~/.../test4.md:24
 [38] vector_mode_dual_eval!
    @ ~/.julia/packages/ForwardDiff/UBbGT/src/apiutils.jl:24 [inlined]
 [39] vector_mode_gradient(f::typeof(loss), x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:91
 [40] gradient
    @ ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:20 [inlined]
 [41] gradient(f::typeof(loss), x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:17
 [42] gradient(f::typeof(loss), x::Vector{Float64})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:17
 [43] top-level scope
    @ ~/.../test4.md:32
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/.../Project.toml`
⌃ [2169fc97] AlgebraicMultigrid v0.5.1
  [4fba245c] ArrayInterface v7.18.0
  [aae01518] BandedMatrices v1.9.1
  [ffab5731] BlockBandedMatrices v0.13.4
  [0a1fb500] BlockDiagonals v0.1.42
  [0c46a032] DifferentialEquations v7.16.0
  [f6369f11] ForwardDiff v0.10.38
  [63c18a36] KernelAbstractions v0.9.34
  [7ed4a6bd] LinearSolve v3.3.1
  [91a5bcdd] Plots v1.40.9
  [33c8b6b6] ProgressLogging v0.1.4
  [1ed8b502] SciMLSensitivity v7.74.0
  [2f01184e] SparseArrays v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

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

  [47edcb42] ADTypes v1.13.0
  [621f4979] AbstractFFTs v1.5.0
  [7d9f7c33] Accessors v0.1.41
  [79e6a3ab] Adapt v4.1.1
⌃ [2169fc97] AlgebraicMultigrid v0.5.1
  [66dad0bd] AliasTables v1.1.3
  [a95523ee] AlmostBlockDiagonals v0.1.10
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.0
  [a9b6321e] Atomix v1.1.0
  [aae01518] BandedMatrices v1.9.1
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.4.0
  [ffab5731] BlockBandedMatrices v0.13.4
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  [764a87c0] BoundaryValueDiffEq v5.15.0
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  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.38
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  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [0c68f7d7] GPUArrays v11.2.2
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.2.0
  [28b8d3ca] GR v0.73.13
  [c145ed77] GenericSchur v0.5.4
  [86223c79] Graphs v1.12.0
  [42e2da0e] Grisu v1.0.2
  [cd3eb016] HTTP v1.10.15
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  [50262376] OrdinaryDiffEqDefault v1.3.0
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  [a759f4b9] TimerOutputs v0.5.26
  [9f7883ad] Tracker v0.2.37
  [3bb67fe8] TranscodingStreams v0.11.3
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.22.0
  [45397f5d] UnitfulLatexify v1.6.4
  [013be700] UnsafeAtomics v0.3.0
  [41fe7b60] Unzip v0.2.0
  [19fa3120] VertexSafeGraphs v0.2.0
⌃ [e88e6eb3] Zygote v0.6.75
  [700de1a5] ZygoteRules v0.2.7
  [6e34b625] Bzip2_jll v1.0.9+0
  [83423d85] Cairo_jll v1.18.2+1
  [ee1fde0b] Dbus_jll v1.14.10+0
  [7cc45869] Enzyme_jll v0.0.172+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.6.5+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [a3f928ae] Fontconfig_jll v2.15.0+0
  [d7e528f0] FreeType2_jll v2.13.3+1
  [559328eb] FriBidi_jll v1.0.16+0
  [0656b61e] GLFW_jll v3.4.0+2
  [d2c73de3] GR_jll v0.73.13+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.82.4+0
  [3b182d85] Graphite2_jll v1.3.14+1
  [2e76f6c2] HarfBuzz_jll v8.5.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [aacddb02] JpegTurbo_jll v3.1.1+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.1+0
  [dad2f222] LLVMExtra_jll v0.0.35+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.3+0
⌅ [e9f186c6] Libffi_jll v3.2.2+2
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.7.0+0
  [7add5ba3] Libgpg_error_jll v1.51.1+0
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.40.3+0
  [89763e89] Libtiff_jll v4.7.1+0
  [38a345b3] Libuuid_jll v2.40.3+0
  [856f044c] MKL_jll v2025.0.1+1
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.16+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.56.1+0
⌅ [30392449] Pixman_jll v0.43.4+0
⌅ [c0090381] Qt6Base_jll v6.7.1+1
⌅ [629bc702] Qt6Declarative_jll v6.7.1+2
⌅ [ce943373] Qt6ShaderTools_jll v6.7.1+1
⌃ [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.5.1+0
⌅ [fb77eaff] Sundials_jll v5.2.3+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+2
  [2381bf8a] Wayland_protocols_jll v1.36.0+0
  [02c8fc9c] XML2_jll v2.13.6+0
  [aed1982a] XSLT_jll v1.1.42+0
  [ffd25f8a] XZ_jll v5.6.4+1
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+3
  [0c0b7dd1] Xorg_libXau_jll v1.0.12+0
  [935fb764] Xorg_libXcursor_jll v1.2.3+0
  [a3789734] Xorg_libXdmcp_jll v1.1.5+0
  [1082639a] Xorg_libXext_jll v1.3.6+3
  [d091e8ba] Xorg_libXfixes_jll v6.0.0+0
  [a51aa0fd] Xorg_libXi_jll v1.8.2+0
  [d1454406] Xorg_libXinerama_jll v1.1.5+0
  [ec84b674] Xorg_libXrandr_jll v1.5.4+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+1
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.2+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+3
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+1
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+1
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.1+0
  [3161d3a3] Zstd_jll v1.5.7+0
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.56.3+0
  [1a1c6b14] gperf_jll v3.1.1+1
  [a4ae2306] libaom_jll v3.11.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.46+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+2
  [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
  [1a1011a3] SharedArrays 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 v0.8.1+2
  [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

• Output of versioninfo()

Julia Version 1.11.2
Commit 5e9a32e7af2 (2024-12-01 20:02 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 8 × Apple M1
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 1

Additional context

My understanding from the debugger is that the cache for du is not getting converted to dual numbers for some reason.