SciML/ModelingToolkit.jl
A Julia framework for symbolic-numeric scientific computing with automatic parallelization and differentiation for scientific machine learning.

ModelingToolkit.jl provides a high-level symbolic modeling framework for scientific machine learning, enabling users to define models for symbolic preprocessing and automatic transformations. It generates optimized code for Jacobians, Hessians, and other model components with automatic sparsification and parallelization. The system handles transformations like index reduction to prepare differential equation models for numerical solvers.