build(deps): update ModelingToolkit requirement from 9 to 9, 11.27 in the all-julia-packages group across 1 directory

[dependabot]

Updates the requirements on ModelingToolkit to permit the latest version.
Updates ModelingToolkit to 11.27.0

Changelog

Sourced from ModelingToolkit's changelog.

ModelingToolkit v11 Release Notes

Symbolics@7 and SymbolicUtils@4 compatibility

SymbolicUtils version 4 involved a major overhaul of the core symbolic infrastructure, which propagated to Symbolics as Symbolics version 7. ModelingToolkit has now updated to these versions. This includes significant type-stability improvements, enabling precompilation of large parts of the symbolic infrastructure and faster TTFX. It is highly recommended to read the Release Notes for SymbolicUtils@4 and the doc page describing the new variant structure before these release notes.

As part of these changes, ModelingToolkit has changed how some data is represented to allow precompilation. Notably, variable => value mappings (such as guesses) are stored as an AbstractDict{SymbolicT, SymbolicT}. Here, SymbolicT is a type that comes from Symbolics.jl, and is the type for all unwrapped symbolic values. This means that any non-symbolic values are stored as SymbolicUtils.Const variants. Mutation such as guesses(sys)[x] = 1.0 is still possible, and values are automatically converted. However, obtaining the value back requires usage of SymbolicUtils.unwrap_const or Symbolics.value.

Following is a before/after comparison of the TTFX for the most common operations in ModelingToolkit.jl. Further improvements are ongoing. Note that the timings do depend on many factors such as the exact system used, types passed to constructor functions, other packages currently loaded in the session, presence of array variables/equations, whether index reduction is required, and the behavior of various passes in mtkcompile. However, the numbers are good representations of the kinds of performance improvements that are possible due to the new infrastructure. There will continue to be improvements as this gets more extensive testing and we are better able to identify bottlenecks in compilation.

System constructor

The time to call System, not including the time taken for @variables or building the equations.

Before:

  0.243758 seconds (563.80 k allocations: 30.613 MiB, 99.48% compilation time: 3% of which was recompilation)
elapsed time (ns):  2.43757958e8
gc time (ns):       0
bytes allocated:    32099616
pool allocs:        563137
non-pool GC allocs: 16
malloc() calls:     651
free() calls:       0
minor collections:  0
full collections:   0

After:

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