`IntervalNonlinearProblem` fails with `Zygote`

[mchitre]

Description of the bug 🐞

IntervalNonlinearProblem fails with Zygote as shown in the MWE below.

Presumably, it is hitting the AbstractNonlinearProblem and looking for the u0. @ChrisRackauckas thinks we specialized IntervalNonlinearProblem with forward mode by maybe missed something around reverse mode optimizations there.

Minimal Reproducible Example 👇

julia> using NonlinearSolve, Zygote

julia> f(x, p) = x^2 - p
julia> g(p) = solve(IntervalNonlinearProblem(f, (1.0, 3.0), p[1])).u

julia> g([4.1])
2.024845673131659

julia> Zygote.gradient(g, [4.1])
ERROR: type IntervalNonlinearProblem has no field u0
Stacktrace:
 [1] getproperty
   @ ~/.julia/packages/SciMLBase/c6Noy/src/problems/problem_interface.jl:5 [inlined]
 [2] (::SciMLBaseZygoteExt.var"#solu_adjoint#126"{SciMLBase.NonlinearSolution{…}})(Δ::Float64)
   @ SciMLBaseZygoteExt ~/.julia/packages/SciMLBase/c6Noy/ext/SciMLBaseZygoteExt.jl:241
 [3] (::SciMLBaseZygoteExt.var"#239#back#127"{SciMLBaseZygoteExt.var"#solu_adjoint#126"{…}})(Δ::Float64)
   @ SciMLBaseZygoteExt ~/.julia/packages/ZygoteRules/CkVIK/src/adjoint.jl:72
 [4] g
   @ ./REPL[11]:1 [inlined]
 [5] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Float64)
   @ Zygote ~/.julia/packages/Zygote/HdT4O/src/compiler/interface2.jl:0
 [6] (::Zygote.var"#88#89"{Zygote.Pullback{Tuple{…}, Tuple{…}}})(Δ::Float64)
   @ Zygote ~/.julia/packages/Zygote/HdT4O/src/compiler/interface.jl:97
 [7] gradient(f::Function, args::Vector{Float64})
   @ Zygote ~/.julia/packages/Zygote/HdT4O/src/compiler/interface.jl:154
 [8] top-level scope
   @ REPL[14]:1

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

[8913a72c] NonlinearSolve v4.6.0
[e88e6eb3] Zygote v0.7.6

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

[47edcb42] ADTypes v1.14.0
[621f4979] AbstractFFTs v1.5.0
[7d9f7c33] Accessors v0.1.42
[79e6a3ab] Adapt v4.3.0
[4fba245c] ArrayInterface v7.18.0
[4c555306] ArrayLayouts v1.11.1
[62783981] BitTwiddlingConvenienceFunctions v0.1.6
[70df07ce] BracketingNonlinearSolve v1.1.3
[2a0fbf3d] CPUSummary v0.2.6
[082447d4] ChainRules v1.72.3
[d360d2e6] ChainRulesCore v1.25.1
[fb6a15b2] CloseOpenIntervals v0.1.13
[38540f10] CommonSolve v0.2.4
[bbf7d656] CommonSubexpressions v0.3.1
[f70d9fcc] CommonWorldInvalidations v1.0.0
[34da2185] Compat v4.16.0
[a33af91c] CompositionsBase v0.1.2
[2569d6c7] ConcreteStructs v0.2.3
[187b0558] ConstructionBase v1.5.8
[adafc99b] CpuId v0.3.1
[a8cc5b0e] Crayons v4.1.1
[9a962f9c] DataAPI v1.16.0
[864edb3b] DataStructures v0.18.22
[e2d170a0] DataValueInterfaces v1.0.0
[2b5f629d] DiffEqBase v6.167.2
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[a0c0ee7d] DifferentiationInterface v0.6.52
[ffbed154] DocStringExtensions v0.9.4
[4e289a0a] EnumX v1.0.5
[f151be2c] EnzymeCore v0.8.8
[e2ba6199] ExprTools v0.1.10
[55351af7] ExproniconLite v0.10.14
[7034ab61] FastBroadcast v0.3.5
[9aa1b823] FastClosures v0.3.2
[a4df4552] FastPower v1.1.2
[1a297f60] FillArrays v1.13.0
[6a86dc24] FiniteDiff v2.27.0
[f6369f11] ForwardDiff v1.0.1
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v0.1.3
[46192b85] GPUArraysCore v0.2.0
[7869d1d1] IRTools v0.4.14
[615f187c] IfElse v0.1.1
[3587e190] InverseFunctions v0.1.17
[92d709cd] IrrationalConstants v0.2.4
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.7.0
[ae98c720] Jieko v0.2.1
[ba0b0d4f] Krylov v0.10.0
[b964fa9f] LaTeXStrings v1.4.0
[10f19ff3] LayoutPointers v0.1.17
[5078a376] LazyArrays v2.6.1
[87fe0de2] LineSearch v0.1.4
[7ed4a6bd] LinearSolve v3.8.0
[2ab3a3ac] LogExpFunctions v0.3.29
[1914dd2f] MacroTools v0.5.16
[d125e4d3] ManualMemory v0.1.8
[bb5d69b7] MaybeInplace v0.1.4
[2e0e35c7] Moshi v0.3.5
[46d2c3a1] MuladdMacro v0.2.4
[77ba4419] NaNMath v1.1.3
[8913a72c] NonlinearSolve v4.6.0
[be0214bd] NonlinearSolveBase v1.5.3
[5959db7a] NonlinearSolveFirstOrder v1.3.1
[9a2c21bd] NonlinearSolveQuasiNewton v1.2.1
[26075421] NonlinearSolveSpectralMethods v1.1.1
[bac558e1] OrderedCollections v1.8.0
[d96e819e] Parameters v0.12.3
[f517fe37] Polyester v0.7.16
[1d0040c9] PolyesterWeave v0.2.2
⌅ [aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.4.3
[08abe8d2] PrettyTables v2.4.0
[c1ae055f] RealDot v0.1.0
[3cdcf5f2] RecipesBase v1.3.4
[731186ca] RecursiveArrayTools v3.31.2
[189a3867] Reexport v1.2.2
[ae029012] Requires v1.3.1
[7e49a35a] RuntimeGeneratedFunctions v0.5.13
[94e857df] SIMDTypes v0.1.0
[0bca4576] SciMLBase v2.84.0
[19f34311] SciMLJacobianOperators v0.1.2
[c0aeaf25] SciMLOperators v0.3.13
[53ae85a6] SciMLStructures v1.7.0
[efcf1570] Setfield v1.1.2
[727e6d20] SimpleNonlinearSolve v2.2.2
[dc90abb0] SparseInverseSubset v0.1.2
[0a514795] SparseMatrixColorings v0.4.18
[276daf66] SpecialFunctions v2.5.1
[aedffcd0] Static v1.2.0
[0d7ed370] StaticArrayInterface v1.8.0
[1e83bf80] StaticArraysCore v1.4.3
[10745b16] Statistics v1.11.1
[7792a7ef] StrideArraysCore v0.5.7
[892a3eda] StringManipulation v0.4.1
[09ab397b] StructArrays v0.7.1
[2efcf032] SymbolicIndexingInterface v0.3.39
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.12.0
[8290d209] ThreadingUtilities v0.5.3
[a759f4b9] TimerOutputs v0.5.28
[781d530d] TruncatedStacktraces v1.4.0
[3a884ed6] UnPack v1.0.2
[e88e6eb3] Zygote v0.7.6
[700de1a5] ZygoteRules v0.2.7
[1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
[856f044c] MKL_jll v2025.0.1+1
[efe28fd5] OpenSpecFun_jll v0.5.6+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
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.11.0
[de0858da] Printf v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization 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 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 10 × Apple M1 Pro
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)