Tutorial example fails

[ranjanan]

Describe the bug 🐞

This SciML tutorial fails with InitialError.

Minimal Reproducible Example 👇

# Import the packages
using ModelingToolkit, NonlinearSolve

# Define the nonlinear system
@variables x=1.0 y=0.0 z=0.0
@parameters σ=10.0 ρ=26.0 β=8 / 3

eqs = [0 ~ σ * (y - x),
    0 ~ x * (ρ - z) - y,
    0 ~ x * y - β * z]
@mtkbuild ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])

# Convert the symbolic system into a numerical system
prob = NonlinearProblem(ns, [])

# Solve the numerical problem
sol = solve(prob, NewtonRaphson())

# Analyze the solution
@show sol[[x, y, z]], sol.resid

Error & Stacktrace ⚠️

julia> # Import the packages
       using ModelingToolkit, NonlinearSolve

julia> @variables x=1.0 y=0.0 z=0.0
3-element Vector{Num}:
 x
 y
 z

julia> @parameters σ=10.0 ρ=26.0 β=8 / 3
3-element Vector{Num}:
 σ
 ρ
 β

julia> eqs = [0 ~ σ * (y - x),
           0 ~ x * (ρ - z) - y,
           0 ~ x * y - β * z]
3-element Vector{Equation}:
 0 ~ (-x + y)*σ
 0 ~ -y + x*(-z + ρ)
 0 ~ x*y - z*β

julia> @mtkbuild ns = NonlinearSystem(eqs, [x, y, z], [σ, ρ, β])

       # Convert the symbolic system into a numerical system
Model ns:
Equations (2):
  2 standard: see equations(ns)
Unknowns (2): see unknowns(ns)
  x [defaults to 1.0]
  z [defaults to 0.0]
Parameters (3): see parameters(ns)
  ρ [defaults to 26.0]
  β [defaults to 2.66667]
  σ [defaults to 10.0]
Observed (1): see observed(ns)

julia> prob = NonlinearProblem(ns, [])

       # Solve the numerical problem
┌ Warning: Initialization system is overdetermined. 1 equations for 0 unknowns. Initialization will default to using least squares. `SCCNonlinearProblem` can only be used for initialization of fully determined systems and hence will not be used here. To suppress this warning pass warn_initialize_determined = false. To make this warning into an error, pass fully_determined = true
└ @ ModelingToolkit ~/.julia/packages/ModelingToolkit/iQ7So/src/systems/diffeqs/abstractodesystem.jl:1349
NonlinearProblem with uType Vector{Float64}. In-place: true
u0: 2-element Vector{Float64}:
 1.0
 0.0

julia> sol = solve(prob, NewtonRaphson())

       # Analyze the solution
retcode: InitialFailure
u: 2-element Vector{Float64}:
 1.0
 0.0

julia> @show sol[[x, y, z]], sol.resid
(sol[[x, y, z]], sol.resid) = ([1.0, 26.0, 0.0], [250.0, 26.0])
([1.0, 26.0, 0.0], [250.0, 26.0])

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

(test) pkg> st
Status `~/Documents/Work/Demos/test/Project.toml`
  [961ee093] ModelingToolkit v9.60.0
  [8913a72c] NonlinearSolve v4.3.0

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

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/Documents/Work/Demos/test/Manifest.toml`
  [47edcb42] ADTypes v1.11.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.41
  [79e6a3ab] Adapt v4.1.1
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.0
  [e2ed5e7c] Bijections v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.3.0
  [70df07ce] BracketingNonlinearSolve v1.1.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.15
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [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
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.161.0
  [459566f4] DiffEqCallbacks v4.2.2
  [77a26b50] DiffEqNoiseProcess v5.24.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.29
  [8d63f2c5] DispatchDoctor v0.4.19
  [31c24e10] Distributions v0.25.116
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [7c1d4256] DynamicPolynomials v0.6.1
  [06fc5a27] DynamicQuantities v1.4.0
  [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
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.26.2
  [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
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.0
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.25
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.0
  [98e50ef6] JuliaFormatter v1.0.62
  [ccbc3e58] JumpProcesses v9.14.1
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.8
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.5
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.3.1
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v2.38.0
  [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
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.60.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.6.1
  [d41bc354] NLSolversBase v7.8.3
  [77ba4419] NaNMath v1.0.3
  [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
  [429524aa] Optim v1.10.0
  [bac558e1] OrderedCollections v1.7.0
  [90014a1f] PDMats v0.11.31
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [27ebfcd6] Primes v0.5.6
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.1
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.27.4
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [9dfe8606] SCCNonlinearSolve v1.0.0
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.70.0
  [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
  [699a6c99] SimpleTraits v0.9.4
  [a2af1166] SortingAlgorithms v1.2.1
  [0a514795] SparseMatrixColorings v0.4.10
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.5.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.10
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.4
  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
  [2efcf032] SymbolicIndexingInterface v0.3.37
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.9.0
  [0c5d862f] Symbolics v6.22.1
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [8ea1fca8] TermInterface v2.0.0
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.26
  [0796e94c] Tokenize v0.5.29
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.22.0
  [a7c27f48] Unityper v0.1.6
  [3d5dd08c] VectorizationBase v0.21.71
  [897b6980] WeakValueDicts v0.1.0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [f50d1b31] Rmath_jll v0.5.1+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
  [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
  [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> versioninfo()
Julia Version 1.11.2
Commit 5e9a32e7af2 (2024-12-01 20:02 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: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_PKG_USE_CLI_GIT = true
  JULIA_PKG_SERVER = internal.juliahub.com

Additional context

Add any other context about the problem here.

[ChrisRackauckas]

Fixed.