Wrong gradient when using `AutoSpecialize` and embedding the `ODEProblem` in a `NamedTuple`

[albertomercurio]

Describe the bug 🐞

I compared the gradient of the ODE with the analytical solution and also with FiniteDifferences.jl. When I specialize the level of the ODE with, e.g., AutoSpecialize or FullSpecialize, and I simultaneously generate the ODEProblem within a NamedTuple, I get a wrong gradient.

More specifically, the gradient is exactly twice the correct one.

Expected behavior

A correct value of the gradient

Minimal Reproducible Example 👇

using LinearAlgebra
using OrdinaryDiffEq
using SciMLSensitivity
using Zygote
using FiniteDifferences
using OrdinaryDiffEq.SciMLBase: FullSpecialize, AutoSpecialize

##

function dudt!(du, u, p, t)
    # dx/dt
    du[1] = u[2]
    # dv/dt
    du[2] = -p[1]^2 * u[1]
    return nothing
end

const u0 = [1.0, 0.0]

function my_prob(p)
    prob = ODEProblem{true, AutoSpecialize}(dudt!, u0, (0.0, 20.0), p, abstol=1e-8, reltol=1e-6)

    return (prob = prob, )
end

function my_fun(p)
    prob = my_prob(p)

    sol = solve(prob.prob, Tsit5())

    return sol.u[end][1]
end

my_fun_analytic(ω) = cos(ω * 20.0)
my_fun_analytic_deriv(ω) = -20.0 * sin(ω * 20.0)

params = [1.0]
my_fun(params) # 0.40808179147463763
my_fun_analytic(1.0) # 0.40808206181339196

##

my_fun_analytic_deriv(1.0) # -18.258905014552553

Zygote.gradient(my_fun_analytic, 1.0) # (-18.258905014552553,)

Zygote.gradient(my_fun, params) # ([-36.51781194303039],)

grad(central_fdm(5, 1), my_fun, params) # ([-18.25890363550605],)

The gradient is correct if I either remove the explicit specialization, or if I return directly the problem instead of the NamedTuple.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/GitHub/Research/Undef/Autodiff QuantumToolbox/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.0
  [13f3f980] CairoMakie v0.13.2
  [082447d4] ChainRules v1.72.3
  [d360d2e6] ChainRulesCore v1.25.1
  [b0b7db55] ComponentArrays v0.15.26
  [7da242da] Enzyme v0.13.35
  [26cc04aa] FiniteDifferences v0.12.32
⌅ [f6369f11] ForwardDiff v0.10.38
  [1dea7af3] OrdinaryDiffEq v6.93.0
  [33c8b6b6] ProgressLogging v0.1.4
  [6c2fb7c5] QuantumToolbox v0.29.1 `~/.julia/dev/QuantumToolbox`
  [731186ca] RecursiveArrayTools v3.31.2
  [37e2e3b7] ReverseDiff v1.16.1
  [c0aeaf25] SciMLOperators v0.3.13
  [1ed8b502] SciMLSensitivity v7.76.0
  [5d786b92] TerminalLoggers v0.1.7
  [e88e6eb3] Zygote v0.7.6

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

Details

Status `~/GitHub/Research/Undef/Autodiff QuantumToolbox/Manifest.toml`
  [47edcb42] ADTypes v1.14.0
  [621f4979] AbstractFFTs v1.5.0
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  [6e4b80f9] BenchmarkTools v1.6.0
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [70df07ce] BracketingNonlinearSolve v1.1.2
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
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  [13f3f980] CairoMakie v0.13.2
  [7057c7e9] Cassette v0.3.14
  [082447d4] ChainRules v1.72.3
  [d360d2e6] ChainRulesCore v1.25.1
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  [35d6a980] ColorSchemes v3.29.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.0
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⌅ [f6369f11] ForwardDiff v0.10.38
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  [d9f16b24] Functors v0.5.2
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  [61eb1bfa] GPUCompiler v1.3.2
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  [692b3bcd] JLLWrappers v1.7.0
  [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
  [b835a17e] JpegTurbo v0.1.6
  [ccbc3e58] JumpProcesses v9.14.2
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  [5ab0869b] KernelDensity v0.6.9
  [ba0b0d4f] Krylov v0.9.10
  [929cbde3] LLVM v9.2.0
  [b964fa9f] LaTeXStrings v1.4.0
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [8cdb02fc] LazyModules v0.3.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [2d8b4e74] LevyArea v1.0.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v3.7.2
  [2ab3a3ac] LogExpFunctions v0.3.29
  [1914dd2f] MacroTools v0.5.15
  [ee78f7c6] Makie v0.22.2
  [20f20a25] MakieCore v0.9.1
  [d125e4d3] ManualMemory v0.1.8
  [dbb5928d] MappedArrays v0.4.2
  [0a4f8689] MathTeXEngine v0.6.2
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [e94cdb99] MosaicViews v0.3.4
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.9.1
  [2774e3e8] NLsolve v4.5.1
  [872c559c] NNlib v0.9.30
  [77ba4419] NaNMath v1.1.3
  [f09324ee] Netpbm v1.1.1
  [8913a72c] NonlinearSolve v4.5.0
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  [5959db7a] NonlinearSolveFirstOrder v1.3.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.2.0
  [26075421] NonlinearSolveSpectralMethods v1.1.0
  [d8793406] ObjectFile v0.4.4
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.16.0
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  [429524aa] Optim v1.12.0
  [3bd65402] Optimisers v0.4.6
  [bac558e1] OrderedCollections v1.8.0
  [1dea7af3] OrdinaryDiffEq v6.93.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.2.0
  [6ad6398a] OrdinaryDiffEqBDF v1.4.0
  [bbf590c4] OrdinaryDiffEqCore v1.22.0
  [50262376] OrdinaryDiffEqDefault v1.3.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.6.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.4.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.5.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.10.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.3.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.3.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.6.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.3.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.9.0
  [2d112036] OrdinaryDiffEqSDIRK v1.3.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.1
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.3.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.3.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [90014a1f] PDMats v0.11.33
  [f57f5aa1] PNGFiles v0.4.4
  [65ce6f38] PackageExtensionCompat v1.0.2
  [19eb6ba3] Packing v0.5.1
  [5432bcbf] PaddedViews v0.5.12
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [eebad327] PkgVersion v0.3.3
  [995b91a9] PlotUtils v1.4.3
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [647866c9] PolygonOps v0.1.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.26
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.10.4
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  [1fd47b50] QuadGK v2.11.2
  [6c2fb7c5] QuantumToolbox v0.29.1 `~/.julia/dev/QuantumToolbox`
  [74087812] Random123 v1.7.0
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⌅ [b22a6f82] FFMPEG_jll v6.1.2+0
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⌃ [7746bdde] Glib_jll v2.82.4+0
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  [075b6546] libsixel_jll v1.10.5+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [c5f90fcd] libwebp_jll v1.5.0+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
  [1270edf5] x264_jll v10164.0.1+0
⌅ [dfaa095f] x265_jll v3.6.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [8bf52ea8] CRC32c 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
  [9abbd945] Profile 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+4
  [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 1.11.4
Commit 8561cc3d68d (2025-03-10 11:36 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × 13th Gen Intel(R) Core(TM) i9-13900KF
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 16 default, 0 interactive, 8 GC (on 32 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 16

[DhairyaLGandhi]

I was able to reproduce this. Something is accumulating gradients twice in the graph, which seems to be related to the NamedTuple itself, since the issue goes away if my_fun returns the ODEProblem directly.

[jClugstor]

The gradient is also correct if you use an unnamed Tuple, so it looks like it's something specifically related to NamedTuple.

[jClugstor]

So I think I've isolated it down to the pullback of kwcall being different between the different constructors for ODEProblem:

using the type parameters (this one doubles the gradient when used):

var"%21" = Zygote._pullback(Zygote.Context(), Core.kwcall, (abstol = 1.0e-8, reltol = 1.0e-6), ODEProblem{true, AutoSpecialize}, dudt!, [1.0, 0.0], (0.0, 20.0), params)
var"%21"[2]

∂(kwcall)

using just ODEProblem (this one gives the right result)

var"%20" = Zygote._pullback(Zygote.Context(), Core.kwcall, (abstol = 1.0e-8, reltol = 1.0e-6), ODEProblem, dudt!, [1.0, 0.0], (0.0, 20.0), params)
var"%20"[2]

(::Zygote.var"#kw_zpullback#58"{SciMLBaseChainRulesCoreExt.var"#ODEProblemAdjoint#14"}) (generic function with 1 method)

@DhairyaLGandhi It looks like the the first one doesn't go through the rrule for the ODEProblem constructor, which for some reason causes p to get accumulated again somewhere?

I think just adding an rrule like

function ChainRulesCore.rrule(::Type{<:ODEProblem{iip, S}, args...; kwargs...) where {iip, S}
    function ODEProblemAdjoint(ȳ)
        (NoTangent(), ȳ.f, ȳ.u0, ȳ.tspan, ȳ.p, ȳ.kwargs, ȳ.problem_type)
    end

    ODEProblem(args...; kwargs...), ODEProblemAdjoint
end

should fix this up, I'll try it out.

[jClugstor]

So that does fix this particular issue, one weird thing though is that if you run the pullback multiple times, it ends up adding the gradient each time you run it, which is actually still the case if you use a version that just returns the problem as well. Not sure if that's another bug.

using LinearAlgebra
using OrdinaryDiffEq
using SciMLSensitivity
using Zygote
using FiniteDifferences
using OrdinaryDiffEq.SciMLBase: FullSpecialize, AutoSpecialize, NoSpecialize

params = [1.0]

function dudt!(du, u, p, t)
    # dx/dt
    du[1] = u[2]
    # dv/dt
    du[2] = -p[1]^2 * u[1]
    return nothing
end

const u0 = [1.0, 0.0]

function non_my_prob(p)
    prob = ODEProblem(dudt!, u0, (0.0, 20.0), p, abstol=1e-8, reltol=1e-6)
    sol = solve(prob, Tsit5())

    return sol.u[end][1]
end

y, back = Zygote._pullback(non_my_prob, params)

back(1.0)    #(nothing, [-18.258905971515194])

back(1.0)    # (nothing, [-36.51781194303039])

back(1.0)    # (nothing, [-54.776717914545586])

[ChrisRackauckas]

Check if it's modifying p or u0 each time?

[DhairyaLGandhi]

That is because it's a mutable

[albertomercurio]

Hello, this error is back again.

[DhairyaLGandhi]

Ref SciML/SciMLBase.jl#1237