ForwardDiff sensitivity: works only if parameter struct has a `length` and parametric type

[Ickaser]

Describe the bug 🐞

Jacobians across an ODE (or DAE) solve, where the parameters are provided as a struct, work only if the struct is parametric and has a defined length.

Expected behavior

Though it is probably not good for performance, I would expect that a parameter struct without careful typing would at least execute. However, it instead errors.

Minimal Reproducible Example 👇

struct ExampleParams
    a
    b
end
pp = ExampleParams(1.0, -2.0)
function dae1!(du, u, p, t)
    du .= [-u[1]*p.b , u[1] - u[2], p.a, u[4]*p.a]
end
daef1! = ODEFunction(dae1!, mass_matrix=Diagonal([1, 0, 1, 1]))
exprob = ODEProblem(daef1!, [1.0, 0.0, 0.0, 1.0], (0.0, 1.0), pp)
exsol = solve(exprob, Rodas3())
ext = range(0, 1, length=40)
exy = exp.(ext*3)
plot(exsol)
scatter!(ext, exy)
function obj_ex1(x,p)
    lprob = remake(exprob, p=ExampleParams(x[1], x[2]))
    @info "check1" lprob lprob.p
    sol = solve(lprob, Rodas3())
    [sum(abs2.(sol(ext, idxs=2) .- exy))] 
end
ForwardDiff.jacobian(x->obj_ex1(x,nothing), [1.0, -2.0])

This produces a MethodError because it's trying to put a Dual in a Vector{Float64} somewhere in the initialization routine.

struct ExampleParamsType{T1, T2}
    a::T1
    b::T2
end
Base.length(pp::ExampleParamsType) = 2 # Throws a MethodError if this is not defined
function obj_ex2(x,p)
    lprob = remake(exprob, p=ExampleParamsType(x[1], x[2]))
    @info "check1" lprob lprob.p
    sol = solve(lprob, Rodas3())
    [sum(abs2.(sol(ext, idxs=2) .- exy))] 
end

ForwardDiff.jacobian(x->obj_ex1(x,nothing), [1.0, -2.0])

This way, however, it works. Very curiously, it does not seem to care about the return value of Base.length(::ExampleParamsType), so long as it is an Int: if I replace it with

Base.length(pp::ExampleParamsType) = 100

then things return just fine, whereas I hit an InexactError if I replace 100 with, say, a NaN.

Error & Stacktrace ⚠️
For the case where the struct is not parametric, here is the error:

ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{var"#99#100", 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:900
  Float64(::IrrationalConstants.Sqrthalfπ)
   @ IrrationalConstants C:\Users\iwheeler\.julia\packages\IrrationalConstants\vp5v4\src\macro.jl:112
  ...

Stacktrace:
  [1] convert(::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{var"#99#100", Float64}, Float64, 2})
    @ Base .\number.jl:7
  [2] setindex!(A::Memory{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{var"#99#100", Float64}, Float64, 2}, i1::Int64)
    @ Base .\genericmemory.jl:234
  [3] unsafe_copyto!(dest::Memory{Float64}, doffs::Int64, src::Memory{ForwardDiff.Dual{…}},
 soffs::Int64, n::Int64)
    @ Base .\genericmemory.jl:144
  [4] unsafe_copyto!
    @ .\genericmemory.jl:124 [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!(dest::Vector{…}, bc::Base.Broadcast.Broadcasted{…})
    @ Base.Broadcast .\broadcast.jl:875
 [12] dae1!(du::Vector{Float64}, u::Vector{Float64}, p::ExampleParams, t::Float64)
    @ Main c:\Users\iwheeler\OneDrive - purdue.edu\Documents\LyoResearch\FulbrightPores\scripts\mwe.jl:20
 [13] ODEFunction
    @ C:\Users\iwheeler\.julia\packages\SciMLBase\VAClc\src\scimlfunctions.jl:2358 [inlined]
 [14] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::OrdinaryDiffEqCore.BrownFullBasicInit{…}, isinplace::Val{…})
    @ OrdinaryDiffEqNonlinearSolve C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqNonlinearSolve\gwScS\src\initialize_dae.jl:380
 [15] _initialize_dae!
    @ C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqCore\gALQU\src\initialize_dae.jl:53 [inlined]
 [16] initialize_dae!
    @ C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqCore\gALQU\src\initialize_dae.jl:40 [inlined]
 [17] initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqCore\gALQU\src\initialize_dae.jl:40
 [18] __init(prob::ODEProblem{…}, alg::Rodas3{…}, 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::Rational{…}, 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_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEqCore.DefaultInit, kwargs::@Kwargs{})
    @ OrdinaryDiffEqCore C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqCore\gALQU\src\solve.jl:514
 [19] __init (repeats 5 times)
    @ C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqCore\gALQU\src\solve.jl:11 [inlined]
 [20] __solve(::ODEProblem{…}, ::Rodas3{…}; kwargs::@Kwargs{})
    @ OrdinaryDiffEqCore C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqCore\gALQU\src\solve.jl:6
 [21] __solve
    @ C:\Users\iwheeler\.julia\packages\OrdinaryDiffEqCore\gALQU\src\solve.jl:1 [inlined]
 [22] #solve_call#44
    @ C:\Users\iwheeler\.julia\packages\DiffEqBase\HW4ge\src\solve.jl:632 [inlined]
 [23] solve_call(_prob::ODEProblem{…}, args::Rodas3{…})
    @ DiffEqBase C:\Users\iwheeler\.julia\packages\DiffEqBase\HW4ge\src\solve.jl:589
 [24] solve_up(prob::ODEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::ExampleParams, args::Rodas3{…}; kwargs::@Kwargs{})
    @ DiffEqBase C:\Users\iwheeler\.julia\packages\DiffEqBase\HW4ge\src\solve.jl:1120
 [25] solve_up
    @ C:\Users\iwheeler\.julia\packages\DiffEqBase\HW4ge\src\solve.jl:1099 [inlined]
 [26] solve(prob::ODEProblem{…}, args::Rodas3{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{})
    @ DiffEqBase C:\Users\iwheeler\.julia\packages\DiffEqBase\HW4ge\src\solve.jl:1036
 [27] solve(prob::ODEProblem{…}, args::Rodas3{…})
    @ DiffEqBase C:\Users\iwheeler\.julia\packages\DiffEqBase\HW4ge\src\solve.jl:1026
 [28] obj_ex1(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#99#100", Float64}, Float64, 2}}, p::Nothing)
    @ Main c:\Users\iwheeler\OneDrive - purdue.edu\Documents\LyoResearch\FulbrightPores\scripts\mwe.jl:27
 [29] #99
    @ c:\Users\iwheeler\OneDrive - purdue.edu\Documents\LyoResearch\FulbrightPores\scripts\mwe.jl:30 [inlined]
 [30] vector_mode_dual_eval!
    @ C:\Users\iwheeler\.julia\packages\ForwardDiff\UBbGT\src\apiutils.jl:24 [inlined]
 [31] vector_mode_jacobian(f::var"#99#100", x::Vector{…}, cfg::ForwardDiff.JacobianConfig{…})
    @ ForwardDiff C:\Users\iwheeler\.julia\packages\ForwardDiff\UBbGT\src\jacobian.jl:129
 [32] jacobian
    @ C:\Users\iwheeler\.julia\packages\ForwardDiff\UBbGT\src\jacobian.jl:22 [inlined]
 [33] jacobian(f::var"#99#100", x::Vector{…}, cfg::ForwardDiff.JacobianConfig{…})
    @ ForwardDiff C:\Users\iwheeler\.julia\packages\ForwardDiff\UBbGT\src\jacobian.jl:19
 [34] jacobian(f::var"#99#100", x::Vector{Float64})
    @ ForwardDiff C:\Users\iwheeler\.julia\packages\ForwardDiff\UBbGT\src\jacobian.jl:19
 [35] top-level scope
    @ c:\Users\iwheeler\OneDrive - purdue.edu\Documents\LyoResearch\FulbrightPores\scripts\mwe.jl:30
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 `C:\Users\iwheeler\OneDrive - purdue.edu\Documents\LyoResearch\FulbrightPores\Project.toml`
⌃ [7d9f7c33] Accessors v0.1.38
  [336ed68f] CSV v0.10.15
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  [f6369f11] ForwardDiff v0.10.38
  [b964fa9f] LaTeXStrings v1.4.0
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  [86014da0] LyoPronto v0.1.1 `C:\Users\iwheeler\.julia\dev\LyoPronto`
⌃ [8913a72c] NonlinearSolve v4.2.0
  [429524aa] Optim v1.10.0
  [91a5bcdd] Plots v1.40.9
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  [9d95f2ec] TypedTables v1.4.6
⌃ [1986cc42] Unitful v1.21.0
  [45397f5d] UnitfulLatexify v1.6.4

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

Status `C:\Users\iwheeler\OneDrive - purdue.edu\Documents\LyoResearch\FulbrightPores\Manifest.toml`
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⌃ [90137ffa] StaticArrays v1.9.8
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
⌃ [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.2
  [f3b207a7] StatsPlots v0.15.7
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.0
⌃ [09ab397b] StructArrays v0.6.21
  [53d494c1] StructIO v0.3.1
  [856f2bd8] StructTypes v1.11.0
⌃ [2efcf032] SymbolicIndexingInterface v0.3.35
  [ab02a1b2] TableOperations v1.2.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
  [8290d209] ThreadingUtilities v0.5.2
⌃ [a759f4b9] TimerOutputs v0.5.25
  [9f7883ad] Tracker v0.2.37
  [3bb67fe8] TranscodingStreams v0.11.3
  [d5829a12] TriangularSolve v0.2.1
  [781d530d] TruncatedStacktraces v1.4.0
  [9d95f2ec] TypedTables v1.4.6
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
⌃ [1986cc42] Unitful v1.21.0
  [45397f5d] UnitfulLatexify v1.6.4
  [013be700] UnsafeAtomics v0.3.0
  [e17b2a0c] UnsafePointers v1.0.0
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.71
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [cc8bc4a8] Widgets v0.6.7
  [efce3f68] WoodburyMatrices v1.0.0
  [76eceee3] WorkerUtilities v1.6.1
⌅ [e88e6eb3] Zygote v0.6.73
  [700de1a5] ZygoteRules v0.2.5
⌅ [68821587] Arpack_jll v3.5.1+1
⌃ [6e34b625] Bzip2_jll v1.0.8+2
  [83423d85] Cairo_jll v1.18.2+1
  [ee1fde0b] Dbus_jll v1.14.10+0
⌅ [7cc45869] Enzyme_jll v0.0.165+0
⌃ [2702e6a9] EpollShim_jll v0.0.20230411+0
⌃ [2e619515] Expat_jll v2.6.4+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
⌃ [f5851436] FFTW_jll v3.3.10+1
⌃ [a3f928ae] Fontconfig_jll v2.13.96+0
⌃ [d7e528f0] FreeType2_jll v2.13.3+0
⌃ [559328eb] FriBidi_jll v1.0.14+0
⌃ [0656b61e] GLFW_jll v3.4.0+1
⌅ [d2c73de3] GR_jll v0.73.8+0
  [78b55507] Gettext_jll v0.21.0+0
⌃ [7746bdde] Glib_jll v2.82.2+0
  [3b182d85] Graphite2_jll v1.3.14+1
⌃ [2e76f6c2] HarfBuzz_jll v8.3.1+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
⌃ [aacddb02] JpegTurbo_jll v3.0.4+0
  [c1c5ebd0] LAME_jll v3.100.2+0
⌃ [88015f11] LERC_jll v4.0.0+0
  [dad2f222] LLVMExtra_jll v0.0.34+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
⌃ [dd4b983a] LZO_jll v2.10.2+1
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.11.0+0
⌃ [7e76a0d4] Libglvnd_jll v1.6.0+0
⌃ [7add5ba3] Libgpg_error_jll v1.50.0+0
  [94ce4f54] Libiconv_jll v1.17.0+1
⌃ [4b2f31a3] Libmount_jll v2.40.2+0
⌃ [89763e89] Libtiff_jll v4.7.0+0
⌃ [38a345b3] Libuuid_jll v2.40.2+0
  [856f044c] MKL_jll v2024.2.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
⌃ [458c3c95] OpenSSL_jll v3.0.15+1
⌃ [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.3+0
⌃ [36c8627f] Pango_jll v1.54.1+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
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
⌃ [a2964d1f] Wayland_jll v1.21.0+1
⌃ [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.5+0
  [aed1982a] XSLT_jll v1.1.42+0
⌃ [ffd25f8a] XZ_jll v5.6.3+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
⌃ [4f6342f7] Xorg_libX11_jll v1.8.6+0
⌃ [0c0b7dd1] Xorg_libXau_jll v1.0.11+1
⌃ [935fb764] Xorg_libXcursor_jll v1.2.0+4
⌃ [a3789734] Xorg_libXdmcp_jll v1.1.4+1
⌃ [1082639a] Xorg_libXext_jll v1.3.6+0
⌃ [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
⌃ [a51aa0fd] Xorg_libXi_jll v1.7.10+4
⌃ [d1454406] Xorg_libXinerama_jll v1.1.4+4
⌃ [ec84b674] Xorg_libXrandr_jll v1.5.2+4
⌃ [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
⌃ [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+1
⌃ [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
⌃ [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [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+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
⌃ [c5fb5394] Xorg_xtrans_jll v1.5.0+1
⌃ [3161d3a3] Zstd_jll v1.5.6+1
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.56.3+0
⌃ [1a1c6b14] gperf_jll v3.1.1+0
⌃ [a4ae2306] libaom_jll v3.9.0+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 v1.6.44+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [f8abcde7] micromamba_jll v1.5.8+0
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
⌃ [d8fb68d0] xkbcommon_jll v1.4.1+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 v1.6.0
  [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 1.11.1
Commit 8f5b7ca12a (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)
Environment:
  JULIA_CONDAPKG_BACKEND = Null
  JULIA_PYTHONCALL_EXE = C:\Users\iwheeler\Miniconda3\python.exe

[ChrisRackauckas]

This is a limitation of ForwardDiff so I'm not sure it's going away. We could set it up with the SciMLStructures.jl interface to slightly generalize it in some cases though.