ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling
This system addresses the challenge of poor performance and stability in numerical modeling for users who may not write optimal code, offering automated improvements without requiring changes from the user.
The authors tackled the problem of generating stable and efficient numerical model implementations from user code by introducing ModelingToolkit, a symbolic equation-based system that applies composable graph transformations. They demonstrated that it can automatically parallelize and perform index reduction on differential-algebraic equation solvers, with reduced models outperforming the Dymola Modelica compiler by 590x at 3% error on an HVAC model.
Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe ModelingToolkit (MTK), a symbolic equation-based modeling system which allows for composable transformations to generate stable, efficient, and parallelized model implementations. MTK blurs the lines of traditional symbolic computing by acting directly on a user's numerical code. We show the ability to apply graph algorithms for automatically parallelizing and performing index reduction on code written for differential-algebraic equation (DAE) solvers, "fixing" the performance and stability of the model without requiring any changes to on the user's part. We demonstrate how composable model transformations can be combined with automated data-driven surrogate generation techniques, allowing machine learning methods to generate accelerated approximate models within an acausal modeling framework. These reduced models are shown to outperform the Dymola Modelica compiler on an HVAC model by 590x at 3\% error. Together, this demonstrates MTK as a system for bringing the latest research in graph transformations directly to modeling applications.