Unexpected results when using parameters in initial conditions

[bspanoghe]

Describe the bug 🐞

When using parameters in the initial values of a model, all instances of the model keep the parameter values of the first instance.

Expected behavior

The parameter values should comply with those input by the user.

Minimal Reproducible Example 👇

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D

function my_module(; name, W_m)
    @parameters W_max = W_m
    @variables W(t) = 0.5*W_max

    eqs = [
        D(W) ~ -W / W_max,
    ]
    return ODESystem(eqs, t; name)
end

@mtkbuild sys = my_module(W_m = 10)
defaults(sys)
@mtkbuild sys2 = my_module(W_m = 5)
defaults(sys2) # W_max still defaults to 10

Error & Stacktrace ⚠️

Not applicable

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

(ModSim) pkg> status
Status `~\ModSim\Project.toml`
  [961ee093] ModelingToolkit v9.61.0
  [1dea7af3] OrdinaryDiffEq v6.90.1

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

Manifest

Status `C:\Users\bspanogh\Documents\Github\Caverns_of_code\Julia\ModSim\Manifest.toml`
  [47edcb42] ADTypes v1.12.1
  [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
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  [2569d6c7] ConcreteStructs v0.2.3
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  [163ba53b] DiffResults v1.1.0
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⌅ [6b7a57c9] Expronicon v0.8.5
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  [d9f16b24] Functors v0.5.2
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  [c145ed77] GenericSchur v0.5.4
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  [ba0b0d4f] Krylov v0.9.9
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  [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 v9.61.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.6.2
  [d41bc354] NLSolversBase v7.8.3
  [77ba4419] NaNMath v1.1.1
  [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 v1.11.0
  [bac558e1] OrderedCollections v1.7.0
  [1dea7af3] OrdinaryDiffEq v6.90.1
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.1.0
  [6ad6398a] OrdinaryDiffEqBDF v1.2.0
  [bbf590c4] OrdinaryDiffEqCore v1.15.1
  [50262376] OrdinaryDiffEqDefault v1.2.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.3.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.2.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.3.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.6.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.2.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.3.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.2.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.4.0
  [2d112036] OrdinaryDiffEqSDIRK v1.2.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.2.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.1.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [90014a1f] PDMats v0.11.32
  [65ce6f38] PackageExtensionCompat v1.0.2
  [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 v1.3.0
  [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
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  [276daf66] SpecialFunctions v2.5.0
  [aedffcd0] Static v1.1.1
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  [7792a7ef] StrideArraysCore v0.5.7
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  [0c5d862f] Symbolics v6.25.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
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  [0dad84c5] ArgTools v1.1.2
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  [56ddb016] Logging v1.11.0
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  [1a1011a3] SharedArrays v1.11.0
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  [2f01184e] SparseArrays v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
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  [8dfed614] Test v1.11.0
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  [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 d63adeda50 (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 12 × 12th Gen Intel(R) Core(TM) i7-1265U
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 12 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

Additional context

I suspect the changes in system initialization underlie this issue and it may be related to #3318 and #3346.
Using the defaults keyword to specify initial values fixes the issue:

function my_module(; name, W_m)
    @parameters W_max = W_m
    @variables W(t)

    eqs = [
        D(W) ~ -W / W_max,
    ]
    return ODESystem(eqs, t; name, defaults = [W => 0.5*W_max])
end

@mtkbuild sys = my_module(W_m = 10)
defaults(sys)
@mtkbuild sys2 = my_module(W_m = 5)
defaults(sys2) # W_max correctly defaults to 5

I'm not sure if I'm simply doing initialization incorrectly with the original MRE or if this is indeed unintended behavior?

[AayushSabharwal]

Sigh, another hashconsing bug

[AayushSabharwal]

This happens because the default of W is a Num. In hashconsing in isequal_with_metadata, when comparing the metadata of the W thus created and the W with the old default SU can't handle inspecting Nums because it doesn't know they're symbolic and can't unwrap them. So when isequal_with_metadata compares the old 0.5W_max default and new 0.5W_max default it doesn't dispatch to the specialized implementation and falls back to isequal, which of course says the two are equal.

So now the W always has a default of 0.5W_max in which the W_max has a default of 10. Now, when calling ODESystem it inspects the equations to find variables and parameters. Coincidentally, it looks at W first. MTK adds W to the list of unknowns, then inspects inside the default of W to find parameters used therein. Thus it finds the old W_max with a default of 10 and adds it to the list of parameters. When it re-discovers W_max in the equation, MTK ignores it. Then, when parsing defaults from variable metadata MTK looks at the W_max with a default of 10 instead of the one with a default of 2.

I can "fix" this by unwrapping in Symbolics.setdefaultval but this is essentially the same problem that plagues Symbolics CI currently - SU doesn't know Nums are symbolic and treats them like numbers. If SU has an unwrap equivalent it can make sure to unwrap wherever necessary to know it's operating on the right thing.