casadi VS MomentClosure.jl

Interface for several solvers and integrators.

Howdy! Collocation methods can be... tricky. For NMPC control of vehicles, success has been had using direct multiple shooting. Also easier to implement and more intuitive. In fact, this example from the GH is pretty instructive: https://github.com/casadi/casadi/blob/master/docs/examples/python/race_car.py

JuMP.jl (Julia) or casADi (Python) are good choices.

Python is not mature in this area. If you ask Google what Simulink for Python is, you get responses that point to dead libraries that were never feature complete and slow. The absolute closest is CASADI which is nice for some things but doesn't even have a true causal modeling interface and is mostly abandoned by the developers (they put a patch in every now and then, but just look at the commit graph), and it's slow compared to the Julia tools, so much so that PyBAMM is interfacing with ModelingToolkit.jl in Julia for a performance boost. Python is not the place to be for causal/acausal modeling or controls. Anyone who is saying "Python is mature" here is saying it in the abstract and not in the context of your actual question. Yes, Python has web development frameworks. No it does not have good libraries for tons of areas (control, acausal modeling, pharmacometrics, etc.).

ModelingToolkit.jl adds a different spin on this by noting what makes a good modeling system isn't top down but a system that allows for bottom up contributions. ModelingToolkit is built on Symbolics.jl which uses OSCAR.jl etc., so every time the symbolics community gets better ModelingToolkit.jl gets better. It connects to the whole SciML ecosystem, so any improvement to any of the SciML interface packages is directly an improvement to ModelingToolkit.jl. ModelingToolkit is made to be a set of composable compiler abstractions called transformations, so anyone can add new packages that do new transformations that improve the ecosystem. One that I really like is MomentClosure.jl which symbolically transforms stochastic ModelingToolkit models (ReactionSystem) to approximate symbolic ODESystem models of the moments. And there's domain-specific langauges like Catalyst.jl being built on the interface to give more ways to build models, which is spawning the biocommunity to make model importers into the symbolic forms, when then feeds more ODE models into the same compiler. JuliaSim is then building on this ecosystem, adding cloud infrastructure that is special-purpose made for doing parallel computations of these models, automatic symbolic model discovery from data, automatic generation of approximate models with machine learning, and tying the Julia Computing compiler team into the web that is building this ecosystem.