I am hoping this also opens up more opportunity to leverage Lisp's symbolic powers. I had great fun with Structure and Interpretation of Classical Mechanics (SICM), and recently a paper on analyzing music using symbolic regression [0], and another on symbolic regression with Lisp [1]. Julia and CL seem perfect for this with Mathematica as another option for quickly playing with ideas.

Yeah, Julia does great in this domain. DataDrivenDiffEq.jl (https://datadriven.sciml.ai/) is a comprehensive symbolic regression package out there, which pulls together all of what's mentioned in the article (SINDy and variants, EQSearch, SymbolicRegression.jl (which is the core of PySR), OccamNet, etc.) all into a single API to allow comparisons between each of the methods.

The Julia automated discovery of physical equations work showcases these symbolic regression techniques quite heavily, for example in the State of SciML talk (https://www.youtube.com/watch?v=eSeY4K4bITI) we discuss how this has been used now across hundreds of different scientific use cases. The universal differential equations paper which describes the Julia SciML organization (https://arxiv.org/abs/2001.04385) demonstrates these cases where neural networks in differential equations are mixed with symbolic regression to allow for mixing prior physical knowledge with data for discovering just the unknown higher order physical equations. And there's a lot more directions we're going next.

eggy

Chris, the work of you and others on Julia is nothing short of amazing. Thanks! I tried Julia when it first came out, and then picked it up again to replace my MATLAB habit, and I have not looked back. I can't wait until the sims.jl package and others can be used like Simulink/Modelica.

ChrisRackauckas

The thing to watch in the space of Simulink/Modelica is https://github.com/SciML/ModelingToolkit.jl . It's an acausal modeling system similar to Modelica (though extended to things like SDEs, PDEs, and nonlinear optimization), and has a standard library (https://github.com/SciML/ModelingToolkitStandardLibrary.jl) similar to the MSL. There's still a lot to do, but it's pretty functional at this point. The two other projects to watch are FunctionalModels.jl (https://github.com/tshort/FunctionalModels.jl, which is the renamed Sims.jl), which is built using ModelingToolkit.jl and puts a more functional interface on it. Then there's Modia.jl (https://github.com/ModiaSim/Modia.jl) which had a complete rewrite not too long ago, and in its new form it's fairly similar to ModelingToolkit.jl and the differences are more in the details. For causal modeling similar to Simulink, there's Causal.jl (https://github.com/zekeriyasari/Causal.jl) which is fairly feature-complete, though I think a lot of people these days are going towards acausal modeling instead so flipping Simulink -> acausal, and in that transition picking up Julia, is what I think is the most likely direction (and given MTK has gotten 40,000 downloads in the last year, I think there's good data backing it up).

And quick mention to bring it back to the main thread here, the DataDrivenDiffEq symbolic regression API gives back Symbolics.jl/ModelingToolkit.jl objects, meaning that the learned equations can be put directly into the simulation tools or composed with other physical models. We're really trying to marry this process modeling and engineering world with these "newer" AI tools.