Wrong gradient value when using `EnzymeAdjoint` and `SciMLOperators`

[albertomercurio]

Describe the bug 🐞

The value of the gradient is wrong when using sensealg= EnzymeAdjoint and SciMLOperators.

Expected behavior

A correct value of the gradient.

Minimal Reproducible Example 👇

using LinearAlgebra
using SparseArrays
using OrdinaryDiffEq
using SciMLOperators
using Enzyme
using SciMLSensitivity

const T = Float64

coef1(a, u, p, t) = -p[1]
coef2(a, u, p, t) = p[2]

A1_data = sparse(T[0.0 1.0; 0.0 0.0])
A2_data = sparse(T[0.0 0.0; 1.0 0.0])
c1 = ScalarOperator(one(T), coef1)
c2 = ScalarOperator(one(T), coef2)

const U = c1 * MatrixOperator(A1_data) + c2 * MatrixOperator(A2_data)

function my_fun(p)
    x = T[3.0, 4.0]
    prob = ODEProblem{true}(U, x, (0.0, 100.0), p)
    sol = solve(prob, Tsit5(), save_everystep=false, 
        # sensealg=BacksolveAdjoint(autojacvec=EnzymeVJP()) # Works
        sensealg=EnzymeAdjoint(), # Doesn't work
    )
    return real(sol.u[end][end])
end

p = [1.0, 2.0]

dp = Enzyme.make_zero(p)
Enzyme.autodiff(Enzyme.set_runtime_activity(Enzyme.Reverse), my_fun, Active, Duplicated(p, dp))

dp

2-element Vector{Float64}:
 NaN
 NaN

The function should be correctly differentiable, as it works with, e.g., BacksolveAdjoint(autojacvec=EnzymeVJP()).

More interesting, if I use a custom function that does what SciMLOperators do, then it works

const A1 = sparse(T[0.0 1.0; 0.0 0.0])
const A2 = sparse(T[0.0 0.0; 1.0 0.0])

function dudt!(du, u, p, t)
    mul!(du, A1, u, -p[1], zero(T))
    mul!(du, A2, u, p[2], one(T))
    return nothing
end

function my_fun2(p)
    x = T[3.0, 4.0]
    prob = ODEProblem{true}(dudt!, x, (0.0, 100.0), p)
    sol = solve(prob, Tsit5(), save_everystep=false,
        # sensealg=BacksolveAdjoint(autojacvec=EnzymeVJP())
        sensealg=EnzymeAdjoint(),
    )
    return real(sol.u[end][end])
end

dp = Enzyme.make_zero(p)
Enzyme.autodiff(Enzyme.set_runtime_activity(Enzyme.Reverse), my_fun2, Active, Duplicated(p, dp))

dp

2-element Vector{Float64}:
 -284.20560020264855
 -142.2290049970122

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
  [a0c0ee7d] DifferentiationInterface v0.7.9
  [7da242da] Enzyme v0.13.86
  [26cc04aa] FiniteDifferences v0.12.33
  [f6369f11] ForwardDiff v1.2.1
  [b27dd330] GTPSA v1.4.8
  [7ed4a6bd] LinearSolve v3.43.0
  [1dea7af3] OrdinaryDiffEq v6.102.1
  [6c2fb7c5] QuantumToolbox v0.37.0
  [c0aeaf25] SciMLOperators v1.9.0
  [1ed8b502] SciMLSensitivity v7.90.0
  [e88e6eb3] Zygote v0.7.10

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

Status `~/GitHub/Research/Undef/Autodiff QuantumToolbox/Manifest.toml`
  [47edcb42] ADTypes v1.18.0
  [621f4979] AbstractFFTs v1.5.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.4.0
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.20.0
  [4c555306] ArrayLayouts v1.12.0
  [a9b6321e] Atomix v1.1.2
  [6e4b80f9] BenchmarkTools v1.6.0
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [70df07ce] BracketingNonlinearSolve v1.5.0
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.7
  [7057c7e9] Cassette v0.3.14
  [082447d4] ChainRules v1.72.6
  [d360d2e6] ChainRulesCore v1.26.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.18.1
  [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 v0.19.1
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.190.2
  [459566f4] DiffEqCallbacks v4.10.1
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.9
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.122
  [ffbed154] DocStringExtensions v0.9.5
  [4e289a0a] EnumX v1.0.5
  [7da242da] Enzyme v0.13.86
  [f151be2c] EnzymeCore v0.8.14
  [d4d017d3] ExponentialUtilities v1.27.0
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [7a1cc6ca] FFTW v1.10.0
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.0.2
  [a4df4552] FastPower v1.1.3
  [1a297f60] FillArrays v1.14.0
  [6a86dc24] FiniteDiff v2.29.0
  [26cc04aa] FiniteDifferences v0.12.33
  [f6369f11] ForwardDiff v1.2.1
  [f62d2435] FunctionProperties v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.7.2
  [b27dd330] GTPSA v1.4.8
  [c145ed77] GenericSchur v0.5.6
  [86223c79] Graphs v1.13.1
  [076d061b] HashArrayMappedTries v0.2.0
  [34004b35] HypergeometricFunctions v0.3.28
  [7869d1d1] IRTools v0.4.15
  [615f187c] IfElse v0.1.1
  [40713840] IncompleteLU v0.2.1
  [d25df0c9] Inflate v0.1.5
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.1
⌅ [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
  [ccbc3e58] JumpProcesses v9.19.1
  [63c18a36] KernelAbstractions v0.9.38
  [ba0b0d4f] Krylov v0.10.2
  [929cbde3] LLVM v9.4.4
  [b964fa9f] LaTeXStrings v1.4.0
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.8.0
  [2d8b4e74] LevyArea v1.0.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.4.0
  [7ed4a6bd] LinearSolve v3.43.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.10.0
  [2774e3e8] NLsolve v4.5.1
  [872c559c] NNlib v0.9.31
  [77ba4419] NaNMath v1.1.3
  [8913a72c] NonlinearSolve v4.12.0
  [be0214bd] NonlinearSolveBase v2.0.0
  [5959db7a] NonlinearSolveFirstOrder v1.9.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.10.0
  [26075421] NonlinearSolveSpectralMethods v1.5.0
  [d8793406] ObjectFile v0.5.0
  [429524aa] Optim v1.13.2
  [3bd65402] Optimisers v0.4.6
  [bac558e1] OrderedCollections v1.8.1
  [1dea7af3] OrdinaryDiffEq v6.102.1
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.5.0
  [6ad6398a] OrdinaryDiffEqBDF v1.10.1
  [bbf590c4] OrdinaryDiffEqCore v1.36.0
  [50262376] OrdinaryDiffEqDefault v1.8.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.16.1
  [9286f039] OrdinaryDiffEqExplicitRK v1.4.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.8.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.9.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.16.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.4.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.5.0
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.5.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.7.0
  [521117fe] OrdinaryDiffEqLinear v1.6.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.6.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.7.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.15.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.4.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.6.0
  [5b33eab2] OrdinaryDiffEqPRK v1.4.0
  [04162be5] OrdinaryDiffEqQPRK v1.4.0
  [af6ede74] OrdinaryDiffEqRKN v1.5.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.18.1
  [2d112036] OrdinaryDiffEqSDIRK v1.7.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.7.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.6.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.4.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.7.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.5.0
  [79d7bb75] OrdinaryDiffEqVerner v1.6.0
  [90014a1f] PDMats v0.11.35
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [e409e4f3] PoissonRandom v0.4.7
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.34
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
⌅ [08abe8d2] PrettyTables v2.4.0
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [6c2fb7c5] QuantumToolbox v0.37.0
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.37.1
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [37e2e3b7] ReverseDiff v1.16.1
  [708f8203] Richardson v1.4.2
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.15
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.120.0
  [19f34311] SciMLJacobianOperators v0.1.11
  [c0aeaf25] SciMLOperators v1.9.0
  [431bcebd] SciMLPublic v1.0.0
  [1ed8b502] SciMLSensitivity v7.90.0
  [53ae85a6] SciMLStructures v1.7.0
  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.9.0
  [699a6c99] SimpleTraits v0.9.5
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.2
  [dc90abb0] SparseInverseSubset v0.1.2
  [0a514795] SparseMatrixColorings v0.4.21
  [276daf66] SpecialFunctions v2.6.1
  [aedffcd0] Static v1.3.0
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
  [2913bbd2] StatsBase v0.34.6
  [4c63d2b9] StatsFuns v1.5.0
  [789caeaf] StochasticDiffEq v6.83.0
  [7792a7ef] StrideArraysCore v0.5.8
  [892a3eda] StringManipulation v0.4.1
  [09ab397b] StructArrays v0.7.1
  [53d494c1] StructIO v0.3.1
⌃ [2efcf032] SymbolicIndexingInterface v0.3.44
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [8290d209] ThreadingUtilities v0.5.5
  [a759f4b9] TimerOutputs v0.5.29
  [9f7883ad] Tracker v0.2.38
  [e689c965] Tracy v0.1.6
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [013be700] UnsafeAtomics v0.3.0
  [e88e6eb3] Zygote v0.7.10
  [700de1a5] ZygoteRules v0.2.7
  [7cc45869] Enzyme_jll v0.0.203+1
  [f5851436] FFTW_jll v3.3.11+0
  [a4739e29] GTPSA_jll v1.6.1+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [dad2f222] LLVMExtra_jll v0.0.38+0
  [ad6e5548] LibTracyClient_jll v0.9.1+6
  [856f044c] MKL_jll v2025.2.0+0
  [656ef2d0] OpenBLAS32_jll v0.3.29+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [f50d1b31] Rmath_jll v0.5.1+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
  [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
  [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
  [4607b0f0] SuiteSparse
  [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 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 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_NUM_THREADS = 16

[ChrisRackauckas-Claude]

I've isolated this issue to just the f call - it doesn't require SciMLSensitivity at all. The problem is in SciMLOperators' interaction with Enzyme.

Minimal Reproducer (No SciMLSensitivity needed!)

using LinearAlgebra
using SparseArrays
using SciMLOperators
using Enzyme

# Simple test: Just differentiate through a ScalarOperator * MatrixOperator
const T = Float64
A_data = sparse(T[0.0 1.0; 0.0 0.0])

# Create operator that scales matrix by -p[1]
coef(a, u, p, t) = -p[1]
c = ScalarOperator(one(T), coef)
U_operator = c * MatrixOperator(A_data)

# Function using SciMLOperator
function f_operator(p)
    u = T[3.0, 4.0]
    du = similar(u)
    t = 0.0
    U_operator(du, u, p, t)
    return sum(du)  # Should return -p[1] * 4.0 = -4p[1]
end

# Equivalent manual function
const A = sparse(T[0.0 1.0; 0.0 0.0])
function f_manual(p)
    u = T[3.0, 4.0]
    du = similar(u)
    mul!(du, A, u, -p[1], zero(T))
    return sum(du)  # Should return -p[1] * 4.0 = -4p[1]
end

p = [1.0]

println("Forward pass:")
println("  f_operator(p) = ", f_operator(p), " (WRONG - should be -4.0)")
println("  f_manual(p)   = ", f_manual(p), " (CORRECT)")

println("\nGradient:")
dp_op = Enzyme.make_zero(p)
Enzyme.autodiff(Enzyme.set_runtime_activity(Enzyme.Reverse), f_operator, Active, Duplicated(p, dp_op))
println("  df_operator/dp = ", dp_op, " (WRONG - should be [-4.0])")

dp_man = Enzyme.make_zero(p)
Enzyme.autodiff(Enzyme.set_runtime_activity(Enzyme.Reverse), f_manual, Active, Duplicated(p, dp_man))
println("  df_manual/dp   = ", dp_man, " (CORRECT)")

Output

Forward pass:
  f_operator(p) = 1.381398563018217e-309 (WRONG - should be -4.0)
  f_manual(p)   = -4.0 (CORRECT)

Gradient:
  df_operator/dp = [0.0] (WRONG - should be [-4.0])
  df_manual/dp   = [-4.0] (CORRECT)

Analysis

The issue is that when Enzyme tries to differentiate through SciMLOperators:

1. Forward pass produces garbage values (uninitialized memory)
2. Gradients are always zero

The manual implementation using mul! directly works correctly because Enzyme can properly track through standard LinearAlgebra operations.

This is actually a SciMLOperators bug, not a SciMLSensitivity issue. The operator call mechanism in SciMLOperators isn't compatible with Enzyme's AD.

[ChrisRackauckas]

It seems the issue is the forward pass here.