Implicit Function Adjoint Rules for Enzyme

[m-bossart]

I am trying to use Enzyme to differentiate a function which builds and solves a NonlinearProblem. I believ the issue is with the enzyme extension which is why I'm opening the issue here.

Expected behavior I expect the SciMLSensitivity overload for NonlinearProblem to be called by Enzyme when differentiating.

Minimal Reproducible Example 👇

using SciMLSensitivity
using NonlinearSolve
using Enzyme
using Zygote
using NonlinearSolve
using Test

function nonlinearf(du, u, p)
    du[1] = u[1] .- p[1]
    nothing 
end 
p = [1.0]
function f(p)
    prob_nl = NonlinearProblem{true}(nonlinearf, [0.0], p)
    sol_nl = solve(prob_nl, TrustRegion(); abstol = 1e-9, reltol=1e-9)
    return sol_nl.u[1] * 2 
end 

dp = zeros(1)
dp_zygote = Zygote.gradient(f, p)[1]    #Zygote Works
Enzyme.autodiff(Reverse, f, Active, Duplicated(p, dp))  #Enzyme Fails

Error & Stacktrace ⚠️ I believe this is the problematic line: https://github.com/SciML/DiffEqBase.jl/blob/1658ed0c18e5e8e6776e7da67c52a56af5076fa7/ext/DiffEqBaseEnzymeExt.jl#L33

ERROR: MethodError: no method matching copyto!(::Float64, ::Base.Broadcast.Broadcasted{…})

Closest candidates are:
  copyto!(::AbstractArray, ::Base.Broadcast.Broadcasted{<:Base.Broadcast.AbstractArrayStyle{0}})
   @ Base broadcast.jl:959
  copyto!(::AbstractArray, ::Base.Broadcast.Broadcasted)
   @ Base broadcast.jl:956
  copyto!(::DiffEqArrayOperator, ::Any)
   @ SciMLBase C:\Users\Matt Bossart\.julia\packages\SciMLBase\SDjaO\src\operators\basic_operators.jl:127
  ...

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [d360d2e6] ChainRulesCore v1.23.0
  [b0b7db55] ComponentArrays v0.15.13
  [2b5f629d] DiffEqBase v6.151.1
  [7da242da] Enzyme v0.12.7
  [8913a72c] NonlinearSolve v3.12.0
  [7f7a1694] Optimization v3.25.1
  [42dfb2eb] OptimizationOptimisers v0.2.1
  [1dea7af3] OrdinaryDiffEq v6.78.0
  [f0f68f2c] PlotlyJS v0.18.13
  [295af30f] Revise v3.5.14
  [1ed8b502] SciMLSensitivity v7.59.0
  [e88e6eb3] Zygote v0.6.70

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

[47edcb42] ADTypes v1.2.1
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.36
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.10.0
  [4c555306] ArrayLayouts v1.9.3
  [bf4720bc] AssetRegistry v0.1.0
  [a9b6321e] Atomix v0.1.0
  [d1d4a3ce] BitFlags v0.1.8
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
  [ad839575] Blink v0.12.9
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.5
  [49dc2e85] Calculus v0.5.1
  [7057c7e9] Cassette v0.3.13
  [082447d4] ChainRules v1.66.0
  [d360d2e6] ChainRulesCore v1.23.0
  [fb6a15b2] CloseOpenIntervals v0.1.12
  [da1fd8a2] CodeTracking v1.3.5
  [944b1d66] CodecZlib v0.7.4
  [35d6a980] ColorSchemes v3.25.0
  [3da002f7] ColorTypes v0.11.5
  [c3611d14] ColorVectorSpace v0.10.0
  [5ae59095] Colors v0.12.11
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.15.0
  [b0b7db55] ComponentArrays v0.15.13
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.1
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.5.5
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.151.1
  [459566f4] DiffEqCallbacks v3.6.2
  [77a26b50] DiffEqNoiseProcess v5.21.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.108
  [ffbed154] DocStringExtensions v0.9.3
  [fa6b7ba4] DualNumbers v0.6.8
  [da5c29d0] EllipsisNotation v1.8.0
  [4e289a0a] EnumX v1.0.4
  [7da242da] Enzyme v0.12.7
  [f151be2c] EnzymeCore v0.7.2
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
  [7034ab61] FastBroadcast v0.2.8
  [9aa1b823] FastClosures v0.3.2
⌃ [29a986be] FastLapackInterface v2.0.3
  [1a297f60] FillArrays v1.11.0
  [6a86dc24] FiniteDiff v2.23.1
  [53c48c17] FixedPointNumbers v0.8.5
  [f6369f11] ForwardDiff v0.10.36
  [f62d2435] FunctionProperties v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [de31a74c] FunctionalCollections v0.5.0
  [d9f16b24] Functors v0.4.10
  [0c68f7d7] GPUArrays v10.1.1
  [46192b85] GPUArraysCore v0.1.6
  [61eb1bfa] GPUCompiler v0.26.4
  [c145ed77] GenericSchur v0.5.4
  [86223c79] Graphs v1.11.0
  [cd3eb016] HTTP v1.10.8
  [9fb69e20] Hiccup v0.2.2
  [3e5b6fbb] HostCPUFeatures v0.1.16
  [34004b35] HypergeometricFunctions v0.3.23
  [7869d1d1] IRTools v0.4.14
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.4
  [3587e190] InverseFunctions v0.1.14
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [97c1335a] JSExpr v0.5.4
  [682c06a0] JSON v0.21.4
  [aa1ae85d] JuliaInterpreter v0.9.31
  [ccbc3e58] JumpProcesses v9.11.1
  [ef3ab10e] KLU v0.6.0
  [63c18a36] KernelAbstractions v0.9.19
  [ba0b0d4f] Krylov v0.9.6
  [5be7bae1] LBFGSB v0.4.1
⌅ [929cbde3] LLVM v6.6.3
  [b964fa9f] LaTeXStrings v1.3.1
  [10f19ff3] LayoutPointers v0.1.15
  [50d2b5c4] Lazy v0.15.1
⌅ [5078a376] LazyArrays v1.10.0
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.30.0
  [2ab3a3ac] LogExpFunctions v0.3.27
  [e6f89c97] LoggingExtras v1.0.3
  [bdcacae8] LoopVectorization v0.12.170
  [6f1432cf] LoweredCodeUtils v2.4.6
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
⌅ [a3b82374] MatrixFactorizations v2.2.0
  [bb5d69b7] MaybeInplace v0.1.2
  [739be429] MbedTLS v1.1.9
  [e1d29d7a] Missings v1.2.0
  [46d2c3a1] MuladdMacro v0.2.4
  [ffc61752] Mustache v1.0.19
  [a975b10e] Mux v1.0.2
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [872c559c] NNlib v0.9.17
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.12.0
  [d8793406] ObjectFile v0.4.1
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.14.0
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
  [3bd65402] Optimisers v0.3.3
  [7f7a1694] Optimization v3.25.1
⌃ [bca83a33] OptimizationBase v1.0.0
  [42dfb2eb] OptimizationOptimisers v0.2.1
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.78.0
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [fa939f87] Pidfile v1.3.0
  [a03496cd] PlotlyBase v0.8.19
  [f0f68f2c] PlotlyJS v0.18.13
  [f2990250] PlotlyKaleido v2.2.4
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.14
  [1d0040c9] PolyesterWeave v0.2.1
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.21
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.10.0
  [43287f4e] PtrArrays v1.1.0
  [1fd47b50] QuadGK v2.9.4
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.5.3
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.19.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [37e2e3b7] ReverseDiff v1.15.3
  [295af30f] Revise v3.5.14
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.42
  [0bca4576] SciMLBase v2.38.0
  [c0aeaf25] SciMLOperators v0.3.8
  [1ed8b502] SciMLSensitivity v7.59.0
  [53ae85a6] SciMLStructures v1.2.0
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.1
  [777ac1f9] SimpleBufferStream v1.1.0
  [727e6d20] SimpleNonlinearSolve v1.8.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.19.0
  [dc90abb0] SparseInverseSubset v0.1.2
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [aedffcd0] Static v0.8.10
  [0d7ed370] StaticArrayInterface v1.5.0
  [90137ffa] StaticArrays v1.9.4
  [1e83bf80] StaticArraysCore v1.4.2
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.1
  [789caeaf] StochasticDiffEq v6.65.1
  [7792a7ef] StrideArraysCore v0.5.6
  [09ab397b] StructArrays v0.6.18
  [53d494c1] StructIO v0.3.0
  [2efcf032] SymbolicIndexingInterface v0.3.21
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [62fd8b95] TensorCore v0.1.1
  [5d786b92] TerminalLoggers v0.1.7
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [9f7883ad] Tracker v0.2.34
  [3bb67fe8] TranscodingStreams v0.10.8
  [d5829a12] TriangularSolve v0.2.0
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.1.4
  [3d5dd08c] VectorizationBase v0.21.67
  [19fa3120] VertexSafeGraphs v0.2.0
  [0f1e0344] WebIO v0.8.21
  [104b5d7c] WebSockets v1.6.0
  [cc8bc4a8] Widgets v0.6.6
  [e88e6eb3] Zygote v0.6.70
  [700de1a5] ZygoteRules v0.2.5
⌅ [7cc45869] Enzyme_jll v0.0.111+0
  [1d5cc7b8] IntelOpenMP_jll v2024.1.0+0
  [f7e6163d] Kaleido_jll v0.2.1+0
  [dad2f222] LLVMExtra_jll v0.0.29+0
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
  [856f044c] MKL_jll v2024.1.0+0
  [458c3c95] OpenSSL_jll v3.0.13+1
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [f50d1b31] Rmath_jll v0.4.2+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.0+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2

• Output of versioninfo()

Julia Version 1.10.2
Commit bd47eca2c8 (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 16 × 11th Gen Intel(R) Core(TM) i7-11800H @ 2.30GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =