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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• 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

[1-Bart-1]

I am getting the same issue with a @register_array_symbolic function. Any updates on this issue?

[AayushSabharwal]

@register_array_symbolic won't solve it, but likely exacerbate the problem. The workaround is to scalarize the problematic function call. If @variables x(t)[1:3] is an array unknown, function calls should have f([x[1], x[2], x[3]]) instead of f(x) if they can't be traced into. Otherwise, it's better to not register the function. This is of course very general advice, it's easier to "solve" this problem for specific examples.

The true solution for this requires better support for array symbolics in Symbolics.jl/SymbolicUtils.jl, and then some changes to structural_simplify.