NonlinearSolve.jl
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SciML
`Klement` is not robust to reordering residuals
Describe the bug 🐞
The exact same equations that succeed when reordered cause Klement to retcode with Unstable
Expected behavior
The solve succeeds in both cases.
Minimal Reproducible Example 👇
Without MRE, we would only be able to help you to a limited extent, and attention to the issue would be limited. to know more about MRE refer to wikipedia and stackoverflow.
julia> function f1(du, u, p)
x, z = u
du[1] = -z - (x^2) * z
du[2] = 2(-x - x * z)
end
julia> function f2(du, u, p)
x, z = u
du[2] = -z - (x^2) * z
du[1] = 2(-x - x * z)
end
julia> prob1 = NonlinearProblem(f1, [1.0, 3.0])
NonlinearProblem with uType Vector{Float64}. In-place: true
u0: 2-element Vector{Float64}:
1.0
3.0
julia> prob2 = NonlinearProblem(f2, [1.0, 3.0])
NonlinearProblem with uType Vector{Float64}. In-place: true
u0: 2-element Vector{Float64}:
1.0
3.0
julia> solve(prob1, Klement())
retcode: Unstable
u: 2-element Vector{Float64}:
0.00291531976032966
1.1510494642142364
julia> solve(prob2, Klement())
retcode: Success
u: 2-element Vector{Float64}:
4.873903265527293e-23
8.408481292481392e-27
Error & Stacktrace ⚠️
NA
Environment (please complete the following information):
- Output of
using Pkg; Pkg.status()
[82cc6244] DataInterpolations v8.0.0
[2b5f629d] DiffEqBase v6.169.1
[06fc5a27] DynamicQuantities v1.8.0
⌅ [f6369f11] ForwardDiff v0.10.38
[ccbc3e58] JumpProcesses v9.14.3
[b2108857] Lux v1.12.4
[961ee093] ModelingToolkit v9.73.0 `..`
[f162e290] ModelingToolkitNeuralNets v1.7.0
[16a59e39] ModelingToolkitStandardLibrary v2.19.1
[2edaba10] Nemo v0.49.3
[8913a72c] NonlinearSolve v4.8.0
[2ac3b008] NonlinearSolveHomotopyContinuation v0.1.2
[1dea7af3] OrdinaryDiffEq v6.95.0
[0bca4576] SciMLBase v2.85.0
[53ae85a6] SciMLStructures v1.7.0
[860ef19b] StableRNGs v1.0.2
[90137ffa] StaticArrays v1.9.13
[c3572dad] Sundials v4.28.0
[2efcf032] SymbolicIndexingInterface v0.3.39
[d1185830] SymbolicUtils v3.27.0
[0c5d862f] Symbolics v6.38.0
- Output of
using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Click me
[47edcb42] ADTypes v1.14.0
[c3fe647b] AbstractAlgebra v0.44.11
[398f06c4] AbstractLattices v0.3.1
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.42
[79e6a3ab] Adapt v4.3.0
[66dad0bd] AliasTables v1.1.3
[fb37089c] Arblib v1.3.0
[dce04be8] ArgCheck v2.5.0
[ec485272] ArnoldiMethod v0.4.0
[4fba245c] ArrayInterface v7.18.0
[4c555306] ArrayLayouts v1.11.1
[a9b6321e] Atomix v1.1.1
[e2ed5e7c] Bijections v0.1.9
[62783981] BitTwiddlingConvenienceFunctions v0.1.6
[8e7c35d0] BlockArrays v1.6.2
[70df07ce] BracketingNonlinearSolve v1.2.0
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.6
[00ebfdb7] CSTParser v3.4.3
[082447d4] ChainRules v1.72.3
[d360d2e6] ChainRulesCore v1.25.1
[fb6a15b2] CloseOpenIntervals v0.1.13
[861a8166] Combinatorics v1.0.2
⌅ [a80b9123] CommonMark v0.8.16
[38540f10] CommonSolve v0.2.4
[bbf7d656] CommonSubexpressions v0.3.1
[f70d9fcc] CommonWorldInvalidations v1.0.0
[34da2185] Compat v4.16.0
[b0b7db55] ComponentArrays v0.15.26
[b152e2b5] CompositeTypes v0.1.4
[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
[82cc6244] DataInterpolations v8.0.0
[864edb3b] DataStructures v0.18.22
[e2d170a0] DataValueInterfaces v1.0.0
[8bb1440f] DelimitedFiles v1.9.1
[2b5f629d] DiffEqBase v6.169.1
[459566f4] DiffEqCallbacks v4.4.1
[77a26b50] DiffEqNoiseProcess v5.24.1
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[a0c0ee7d] DifferentiationInterface v0.6.52
[8d63f2c5] DispatchDoctor v0.4.19
[31c24e10] Distributions v0.25.119
[ffbed154] DocStringExtensions v0.9.4
[5b8099bc] DomainSets v0.7.15
[7c1d4256] DynamicPolynomials v0.6.1
[06fc5a27] DynamicQuantities v1.8.0
[fdbdab4c] ElasticArrays v1.2.12
[4e289a0a] EnumX v1.0.5
[f151be2c] EnzymeCore v0.8.8
[d4d017d3] ExponentialUtilities v1.27.0
[e2ba6199] ExprTools v0.1.10
[55351af7] ExproniconLite v0.10.14
[7034ab61] FastBroadcast v0.3.5
[9aa1b823] FastClosures v0.3.2
[442a2c76] FastGaussQuadrature v1.0.2
[a4df4552] FastPower v1.1.2
[1a297f60] FillArrays v1.13.0
[64ca27bc] FindFirstFunctions v1.4.1
[6a86dc24] FiniteDiff v2.27.0
[1fa38f19] Format v1.3.7
⌅ [f6369f11] ForwardDiff v0.10.38
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v0.1.3
[d9f16b24] Functors v0.5.2
[46192b85] GPUArraysCore v0.2.0
[c145ed77] GenericSchur v0.5.5
[c27321d9] Glob v1.3.1
[86223c79] Graphs v1.12.1
[076d061b] HashArrayMappedTries v0.2.0
[f213a82b] HomotopyContinuation v2.14.0
[3e5b6fbb] HostCPUFeatures v0.1.17
[34004b35] HypergeometricFunctions v0.3.28
[615f187c] IfElse v0.1.1
[d25df0c9] Inflate v0.1.5
[18e54dd8] IntegerMathUtils v0.1.2
[8197267c] IntervalSets v0.7.10
[524e6230] IntervalTrees v1.1.0
[3587e190] InverseFunctions v0.1.17
[92d709cd] IrrationalConstants v0.2.4
[c8e1da08] IterTools v1.10.0
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.7.0
[ae98c720] Jieko v0.2.1
⌅ [98e50ef6] JuliaFormatter v1.0.62
[ccbc3e58] JumpProcesses v9.14.3
[63c18a36] KernelAbstractions v0.9.34
[ba0b0d4f] Krylov v0.10.0
[8ac3fa9e] LRUCache v1.6.2
[b964fa9f] LaTeXStrings v1.4.0
[23fbe1c1] Latexify v0.16.7
[10f19ff3] LayoutPointers v0.1.17
[5078a376] LazyArrays v2.6.1
[9c8b4983] LightXML v0.9.1
[87fe0de2] LineSearch v0.1.4
[d3d80556] LineSearches v7.3.0
[9b3f67b0] LinearAlgebraX v0.2.10
[7ed4a6bd] LinearSolve v3.8.0
[2ab3a3ac] LogExpFunctions v0.3.29
[bdcacae8] LoopVectorization v0.12.172
[b2108857] Lux v1.12.4
[bb33d45b] LuxCore v1.2.4
[82251201] LuxLib v1.7.2
[7e8f7934] MLDataDevices v1.9.1
[d8e11817] MLStyle v0.4.17
[1914dd2f] MacroTools v0.5.16
[d125e4d3] ManualMemory v0.1.8
[bb5d69b7] MaybeInplace v0.1.4
[e1d29d7a] Missings v1.2.0
[291d046c] MixedSubdivisions v1.1.5
[961ee093] ModelingToolkit v9.73.0 `..`
[f162e290] ModelingToolkitNeuralNets v1.7.0
[16a59e39] ModelingToolkitStandardLibrary v2.19.1
[7475f97c] Mods v2.2.6
[2e0e35c7] Moshi v0.3.5
[46d2c3a1] MuladdMacro v0.2.4
[3b2b4ff1] Multisets v0.4.5
[102ac46a] MultivariatePolynomials v0.5.7
[d8a4904e] MutableArithmetics v1.6.4
[d41bc354] NLSolversBase v7.9.1
[872c559c] NNlib v0.9.30
[77ba4419] NaNMath v1.1.3
[2edaba10] Nemo v0.49.3
[8913a72c] NonlinearSolve v4.8.0
[be0214bd] NonlinearSolveBase v1.6.0
[5959db7a] NonlinearSolveFirstOrder v1.4.0
[2ac3b008] NonlinearSolveHomotopyContinuation v0.1.2
[9a2c21bd] NonlinearSolveQuasiNewton v1.3.0
[26075421] NonlinearSolveSpectralMethods v1.2.0
[6fe1bfb0] OffsetArrays v1.17.0
[429524aa] Optim v1.12.0
[3bd65402] Optimisers v0.4.6
[bac558e1] OrderedCollections v1.8.0
[1dea7af3] OrdinaryDiffEq v6.95.0
[89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.2.0
[6ad6398a] OrdinaryDiffEqBDF v1.5.0
[bbf590c4] OrdinaryDiffEqCore v1.23.0
[50262376] OrdinaryDiffEqDefault v1.3.0
[4302a76b] OrdinaryDiffEqDifferentiation v1.7.0
[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 v1.6.1
[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 v1.3.0
[e3e12d00] OrdinaryDiffEqStabilizedIRK v1.3.0
[358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
[fa646aed] OrdinaryDiffEqSymplecticRK v1.3.0
[b1df2697] OrdinaryDiffEqTsit5 v1.1.0
[79d7bb75] OrdinaryDiffEqVerner v1.2.0
[90014a1f] PDMats v0.11.34
[d96e819e] Parameters v0.12.3
[2ae35dd2] Permutations v0.4.23
[e409e4f3] PoissonRandom v0.4.4
[f517fe37] Polyester v0.7.16
[1d0040c9] PolyesterWeave v0.2.2
[f27b6e38] Polynomials v4.0.19
[85a6dd25] PositiveFactorizations v0.2.4
[d236fae5] PreallocationTools v0.4.26
⌅ [aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.4.3
[08abe8d2] PrettyTables v2.4.0
[27ebfcd6] Primes v0.5.7
[92933f4c] ProgressMeter v1.10.4
[01f381cc] ProjectiveVectors v1.1.4
[43287f4e] PtrArrays v1.3.0
[1fd47b50] QuadGK v2.11.2
[74087812] Random123 v1.7.0
[fb686558] RandomExtensions v0.4.4
[e6cf234a] RandomNumbers v1.6.0
[c1ae055f] RealDot v0.1.0
[3cdcf5f2] RecipesBase v1.3.4
[731186ca] RecursiveArrayTools v3.32.1
[189a3867] Reexport v1.2.2
[ae029012] Requires v1.3.1
[ae5879a3] ResettableStacks v1.1.1
[286e9d63] RingLists v0.2.9
[79098fc4] Rmath v0.8.0
[7e49a35a] RuntimeGeneratedFunctions v0.5.14
[9dfe8606] SCCNonlinearSolve v1.1.0
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.43
[0bca4576] SciMLBase v2.85.0
[19f34311] SciMLJacobianOperators v0.1.3
[c0aeaf25] SciMLOperators v0.3.13
[53ae85a6] SciMLStructures v1.7.0
[7e506255] ScopedValues v1.3.0
[8e049039] SemialgebraicSets v0.3.3
[efcf1570] Setfield v1.1.2
[55797a34] SimpleGraphs v0.8.6
[727e6d20] SimpleNonlinearSolve v2.3.0
[ec83eff0] SimplePartitions v0.3.3
[cc47b68c] SimplePolynomials v0.2.18
[a6525b86] SimpleRandom v0.3.2
[699a6c99] SimpleTraits v0.9.4
[ce78b400] SimpleUnPack v1.1.0
[a2af1166] SortingAlgorithms v1.2.1
[dc90abb0] SparseInverseSubset v0.1.2
[0a514795] SparseMatrixColorings v0.4.18
[276daf66] SpecialFunctions v2.5.1
[860ef19b] StableRNGs v1.0.2
[aedffcd0] Static v1.2.0
[0d7ed370] StaticArrayInterface v1.8.0
[90137ffa] StaticArrays v1.9.13
[1e83bf80] StaticArraysCore v1.4.3
[10745b16] Statistics v1.11.1
[82ae8749] StatsAPI v1.7.0
[2913bbd2] StatsBase v0.34.4
[4c63d2b9] StatsFuns v1.4.0
[7792a7ef] StrideArraysCore v0.5.7
[892a3eda] StringManipulation v0.4.1
[09ab397b] StructArrays v0.7.1
[c3572dad] Sundials v4.28.0
[2efcf032] SymbolicIndexingInterface v0.3.39
[19f23fe9] SymbolicLimits v0.2.2
[d1185830] SymbolicUtils v3.27.0
[0c5d862f] Symbolics v6.38.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.12.0
[ed4db957] TaskLocalValues v0.1.2
[b36ab563] TaylorDiff v0.3.3
[8ea1fca8] TermInterface v2.0.0
[1c621080] TestItems v1.0.0
[8290d209] ThreadingUtilities v0.5.3
[a759f4b9] TimerOutputs v0.5.28
[0796e94c] Tokenize v0.5.29
[a2a6695c] TreeViews v0.3.0
[410a4b4d] Tricks v0.1.10
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.2
[3a884ed6] UnPack v1.0.2
[1986cc42] Unitful v1.22.0
[a7c27f48] Unityper v0.1.6
[013be700] UnsafeAtomics v0.3.0
[3d5dd08c] VectorizationBase v0.21.71
[897b6980] WeakValueDicts v0.1.0
[d49dbf32] WeightInitializers v1.1.1
[e134572f] FLINT_jll v300.200.100+0
[1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
[94ce4f54] Libiconv_jll v1.18.0+0
[856f044c] MKL_jll v2025.0.1+1
[2ce0c516] MPC_jll v1.3.1+0
[656ef2d0] OpenBLAS32_jll v0.3.29+0
[efe28fd5] OpenSpecFun_jll v0.5.6+0
[f50d1b31] Rmath_jll v0.5.1+0
⌅ [fb77eaff] Sundials_jll v5.2.3+0
⌅ [3428059b] SymEngine_jll v0.9.0+1
⌅ [02c8fc9c] XML2_jll v2.13.6+1
[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
[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
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[781609d7] GMP_jll v6.3.0+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[3a97d323] MPFR_jll v4.2.1+0
[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
[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: macOS (arm64-apple-darwin24.0.0)
CPU: 8 × Apple M2
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)
Threads: 16 default, 2 interactive, 4 GC (on 4 virtual cores)
Environment:
JULIA_PKG_PRECOMPILE_AUTO = 0
JULIA_PKG_USE_CLI_GIT = true
JULIA_PKG_SERVER = https://internal.juliahub.com
Additional context
Add any other context about the problem here.
