Modia and Julia for Grey Box Modeling

Abstract

During the process of modelling an existing dynamic physical system, it may be hard to capture some of the phenomena exactly on the basis of only textbook-equations. With measurement data from the real system, approximators like artificial neural networks can help improve the models. However, simulation and machine learning are usually done in different software applications. A unified environment for modeling, simulation and optimization would be highly valuable. We here present a framework within the Julia programming language that encompasses tools for acausal modeling, automatic differentiation rsp. sensitivity analysis involving solvers for differential equations. We use it to build and evaluate an easily interpretable model based on both physics and data.