Using LevenbergMarquardt for Linear Least Squares Problem Fails after 3.15.1

[nrummel]

Describe the bug 🐞

I have been using NonlinearSolve to solve nonlinear least squares problems in an algorithm I have been developing, but when I upgraded to version v4.x.x the Levenberg Marquardt solver started giving poor results. When I pin the package back at v3.15.1 all my issues resolve, and all the v4.x.x versions I have tried have the behavior below. I can recreate the behavior on a linear least squares problem, I saved the input matrices at the bottom of this issue.

Expected behavior

When I run this code in v3.15.1, the linear least squares problem is solved to a high level of accuracy:

Status `~/nolinearsolveissue/Project.toml`
  [8bb1440f] DelimitedFiles v1.9.1
⌃ [8913a72c] NonlinearSolve v3.15.1 ⚲
Info Packages marked with ⌃ have new versions available and may be upgradable.
[ Info: Relative Error 4.280111795651271e-9

Minimal Reproducible Example 👇

## Load dependencies
using NonlinearSolve: NonlinearLeastSquaresProblem, NonlinearFunction, LevenbergMarquardt, solve
using DelimitedFiles: readdlm
using Pkg
Pkg.status()
## Build linear least square problem for testing 
A = readdlm(joinpath(@__DIR__,"A.csv"),',',Float64)
b = readdlm(joinpath(@__DIR__,"b.csv"),',',Float64)[:]
M,N = size(A)

function r!(r,x, ::Any)
    r .= A*x - b
    nothing 
end
function ∇r!(J, p, ::Any)
    J .= A
    nothing
end
# Run NonlinearSolve.solve
x0 = zeros(N)
sol = solve(
    NonlinearLeastSquaresProblem(
        NonlinearFunction(
            r!;
            jac=∇r!, 
            resid_prototype=zeros(M)
        ),
        x0
    ),
    LevenbergMarquardt()
)

xhat = sol.u
x = A \ b
relErr = norm(xhat- x)/norm(x)
@info "Relative Error $relErr"

Error & Stacktrace ⚠️

Status `~/nolinearsolveissue/Project.toml`
  [8bb1440f] DelimitedFiles v1.9.1
  [8913a72c] NonlinearSolve v4.3.0
[ Info: Relative Error 1.0

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/scratch/wendy/_wendyTriage/nolinearsolveissue/Project.toml`
  [8bb1440f] DelimitedFiles v1.9.1
  [8913a72c] NonlinearSolve v4.3.0

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

Status `~/scratch/wendy/_wendyTriage/nolinearsolveissue/Manifest.toml`
  [47edcb42] ADTypes v1.12.1
  [7d9f7c33] Accessors v0.1.41
  [79e6a3ab] Adapt v4.1.1
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.0
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [70df07ce] BracketingNonlinearSolve v1.1.0
  [2a0fbf3d] CPUSummary v0.2.6
  [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
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.161.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.39
  [ffbed154] DocStringExtensions v0.9.3
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.8.8
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [a4df4552] FastPower v1.1.1
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.27.0
  [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [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
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.9
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.5.1
  [87fe0de2] LineSearch v0.1.4
⌅ [7ed4a6bd] LinearSolve v2.39.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.15
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [46d2c3a1] MuladdMacro v0.2.4
  [77ba4419] NaNMath v1.1.2
  [8913a72c] NonlinearSolve v4.3.0
  [be0214bd] NonlinearSolveBase v1.4.0
  [5959db7a] NonlinearSolveFirstOrder v1.2.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.1.0
  [26075421] NonlinearSolveSpectralMethods v1.1.0
  [6fe1bfb0] OffsetArrays v1.15.0
  [bac558e1] OrderedCollections v1.8.0
  [d96e819e] Parameters v0.12.3
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.29.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.72.2
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.12
  [53ae85a6] SciMLStructures v1.6.1
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v2.1.0
  [0a514795] SparseMatrixColorings v0.4.12
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.5.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [7792a7ef] StrideArraysCore v0.5.7
  [2efcf032] SymbolicIndexingInterface v0.3.37
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.26
  [d5829a12] TriangularSolve v0.2.1
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [3d5dd08c] VectorizationBase v0.21.71
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [856f044c] MKL_jll v2025.0.1+1
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+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
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [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+2
  [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
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 12 × Apple M3 Pro
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)
Threads: 16 default, 0 interactive, 6 GC (on 6 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 16

Additional context

Here are the CSV files for the example:

A.csv

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[ChrisRackauckas]

@avik-pal can you field this one?