Learning the Missing Physics Locally with Modelica and Wolfram Language

Abstract

This paper introduces State-Invariant Hybrid Models (SIHM), a subset of hybrid physics-machine-learning models in which the state vector remains defined by the first-principles Modelica model, while learned components contribute missing physics locally. We qualitatively contrast global residual learning at system level with local residual learning at component level, arguing that local learning better matches the acausal modeling paradigm of Modelica. A tool-agnostic workflow is proposed in which a replaceable dummy component marks the suspected location of missing physics, while compiler-derived structural information identifies the connected states and variables. The workflow is then illustrated in the Wolfram ecosystem on two models to demonstrate the approach's modularity. The results indicate that local SIHM components recover targeted missing effects while preserving the state selection of the original model.