`mtkcompile` performance on large system of ODEs

[sablonl]

For my research, I used ModelingToolkit to port an advection–reaction box model in Julia. When the discretization (and hence the number of equations) is relatively small (say up to ~500), everything works smoothly with the latest version. However, when I increase the resolution of my model (up to 5,000–6,000 equations), compilation never finishes (I stopped mtkcompile after 20 hours).

At the moment, my workaround is to use JuliaSimCompiler.jl with an older version of ModelingToolkit.jl. In this setup, structural_simplify takes around 10 seconds. However, this is not ideal since the package is no longer maintained and is also cumbersome to install (e.g., it requires Julia < 1.10.0).

I ran some tests on a very simplified version of my model and found that compiling a system with O(10^3) very simple equations would still take several hours. See https://github.com/sablonl/MWE_MTK.jl for the MWE.

I know that the latest version is more efficient in terms of symbolic reduction, but the time required makes it completely unusable in my case. So here is my question: are there plans to either match the performance of JuliaSimCompiler in terms of compilation time, propose an alternative fast_mtkcompile option that trades optimization for speed, or enable multithreading during simplification?

Thanks,
L.

[AayushSabharwal]

SymbolicUtils@4 is coming out, which has major performance improvements. It'll take a while to trickle through to MTK, but should help a decent bit. I doubt we'll match JuliaSimCompiler anytime soon, it has a fundamentally different representation of the system, and of expressions in general. It uses its own SSA IR to represent the equations. I have a plan to add an optimization which will help in some cases where differential equations can be trivially torn and should significantly speed up the compile time of index-zero systems. Multithreading isn't a "do this and things are faster" solution - there has to be something significantly parallelizable. I'm not sure where we could use it in the simplification process.