Accelerating the simulation of equation-based models by replacing non-linear algebraic loops with error-controlled machine learning surrogates


  • Andreas Heuermann
  • Philip Hannebohm
  • Matthias Schäfer
  • Bernhard Bachmann



Machine Learning, Dynamic Systems, Surrogate Model, Non-Linear System, Error Control


When simulating a Modelica model, non-linear algebraic loops may be present, which involves solving multiple equations simultaneously. The classical Newton-Raphson method is commonly employed for solving a non-linear equation system (NLS). However, the computational burden of using this method during simulation can be significant. To tackle this issue, utilizing artificial neural networks (ANNs) to approximate the solution of algebraic loops is a promising approach. While ANN surrogates offer fast performance, ensuring the correctness of the computed solution or quantifying reliability can be challenging. This publication presents a prototype, based on the OpenModelica compiler (OMC), that automates the extraction of time-consuming algebraic loops. It generates training data, trains ANNs using machine learning (ML) methods, and replaces the algebraic loops with ANN surrogates in the simulation code. A hybrid approach, combining the trained surrogate with the nonlinear Newton solver, is then used to compute the solution with a desired level of accuracy.