Modeling Coupled Systems Using Port-Hamiltonian Neural Networks

Abstract

Neural networks are able to approximate various physical phenomena, but learning dynamical systems composed of multiple elements remains challenging. One reason for this difficulty is that approximating the entire system with a single multilayer perceptron leads to a large function space to explore. If each element of the system is modeled separately, the search space for functions can be reduced. Given this background, this study proposes the use of Port-Hamiltonian Neural Networks, which, in addition to the inductive bias of traditional models, incorporate modularity. This model describes dynamical systems using port-Hamiltonian systems, enabling not only improved predictive accuracy but also the learning of the connections between elements in the system. The proposed method was evaluated in a coupled system consisting of multiple masses and springs. The results showed that the proposed method has superior prediction performance compared to existing methods and can also learn the connections within the system.