Internal Error: Variables Incorrectly Marked as Zero During Structural Simplification in ODE System

[viniviena]

Describe the bug 🐞
When running a differential equation system using ModelingToolkit, an internal error occurs where variables (N(t))[1] and (N(t))[2] are unexpectedly marked as zero in the equation 0 ~ -H(t) + myfun(T(t), N(t)). This issue arises during the structural transformation call.

Expected behavior
The system should solve the ODE without internal errors, accurately computing the values of the variables (N(t))[1] and (N(t))[2] without them being incorrectly marked as zero.

Minimal Reproducible Example 👇

using ModelingToolkit
using Symbolics
using ModelingToolkit: t_nounits as t, D_nounits as D, scalarize
using OrdinaryDiffEq

myfun(T, x::Vector) =  100.0*T*x[1] + 50.0*T*x[2]
@register_symbolic myfun(T, x::Vector)

function myc(; name)
    vars = @variables begin
       (N(t))[1:2]
       H(t)
       T(t)
    end

    eqs =  [scalarize(D(N) .~ -N), D(H) ~ H/sum(scalarize(N)), 
    H - myfun(T, N) ~ 0.0]     

    ODESystem([eqs...;], t, collect(Iterators.flatten(vars)), []; name)
end

component = myc(; name = :myc)
simple_prob = structural_simplify(component; check_consistency = true)

Error & Stacktrace ⚠️
It is a warning

┌ Warning: Internal error: Variable (N(t))[1] was marked as being in 0 ~ -H(t) + myfun(T(t), N(t)), but was actually zero
└ @ ModelingToolkit.StructuralTransformations C:\Users\vinicius\.julia\packages\ModelingToolkit\Jc09X\src\structural_transformation\utils.jl:233
┌ Warning: Internal error: Variable (N(t))[2] was marked as being in 0 ~ -H(t) + myfun(T(t), N(t)), but was actually zero
└ @ ModelingToolkit.StructuralTransformations C:\Users\vinicius\.julia\packages\ModelingToolkit\Jc09X\src\structural_transformation\utils.jl:233

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `C:\Users\vinicius\OneDrive - NTNU\Research\issuemtk\Project.toml`
  [961ee093] ModelingToolkit v9.35.1
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [0c5d862f] Symbolics v6.5.0

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

Status `C:\Users\vinicius\OneDrive - NTNU\Research\issuemtk\Manifest.toml`
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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 To see why use `status --outdated -m`  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 1.10.4
Commit 48d4fd4843 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 16 × 12th Gen Intel(R) Core(TM) i5-1250P
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

[ChrisRackauckas]

@YingboMa do you know what this warning is about? It's something to do with the symbolic array usage but it seems benign?

[aml5600]

seeing this as well. the equations it warns against include a registered array function which generates a ton of screen output, which shows up during testing.

[Snowd1n]

I have also noticed huge structural_simplify performance hits with this warning. I don't know if it's just due to the potentially large amount of printing to STERROR it does but simplifications can take seconds then I invoke this error and its close to an hour or sometimes longer. I have tested it where I change my vectors from length 5 to length 500 and it changes the simplify time from half a second to 90 mins. Is there a temporary way to disable the warning to fix performance