ModelingToolkit.jl

ModelingToolkit.jl is a modeling language for high-performance symbolic-numeric computation in scientific computing and scientific machine learning. It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. ModelingToolkit can automatically generate fast functions for model components like Jacobians and Hessians, along with automatically sparsifying and parallelizing the computations. Automatic transformations, such as index reduction, can be applied to the model to make it easier for numerical solvers to handle.

Package Overview

ModelingToolkit has 3 layers:

1. The model definition level. This is a high level of syntactic sugar for easily generating ModelingToolkit models. It can be used directly like a DSL for advanced users who want a lot of flexibility in a modeling language. Additionally, automatic tracing functionality allows for easily generating ModelingToolkit models directly from Julia code.
2. The AbstractSystem level. This is the level where content-dependent functionality is added, where models such an ordinary differential equation are represented. At the system level, there are transformations which take one system to another, and targets which output code for numerical solvers.
3. The IR level, also referred to as the direct level. At this level, one directly acts on arrays of Equations, and symbolic expressions to generate functions.

Each level above is built on the level below, giving more context to allow for more automation. For example, the system level allows for automatically generating fast multithreaded sparse Jacobian functions of an ODESystem, which is just calling the sparsity functions and the multithreading capabilities of build_function at the IR level.