Learnable & Interpretable Model Combination in Dynamical Systems Modeling

TL;DR

This paper introduces a learnable, interpretable model combination framework for dynamical systems that integrates various model types, addresses key challenges, and enables gradient-based learning of complex hybrid models.

Contribution

It proposes a novel wildcard architecture capable of expressing mixed models and learning their combination through gradient-based optimization, addressing algebraic loops and discontinuities.

Findings

The architecture can learn and interpret different model combinations.

It effectively handles algebraic loops and event functions.

Experimental results demonstrate successful model learning and comparison.

Abstract

During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning architectures, as well as hybrid models, i.e., the combination of physical simulation models and machine learning. In this work, we briefly discuss which types of model are usually combined in dynamical systems modeling and propose a class of models that is capable of expressing mixed algebraic, discrete, and differential equation-based models. Further, we examine different established, as well as new ways of combining these models from the point of view of system theory and highlight two challenges - algebraic loops and local event functions in discontinuous models - that require a special approach. Finally, we propose a new wildcard architecture that is capable of describing arbitrary combinations of models in an easy-to-interpret fashion that can be learned as part of a gradient-based optimization procedure. In a final experiment, different combination architectures between two models are learned, interpreted, and compared using the methodology and software implementation provided.