Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

TL;DR

This paper introduces port-Hamiltonian neural networks that effectively learn and predict the dynamics of non-autonomous, energy-dissipative, and chaotic physical systems by embedding the port-Hamiltonian formalism into neural networks.

Contribution

It extends Hamiltonian neural networks to non-autonomous systems by incorporating port-Hamiltonian formalism, capturing energy dissipation and time-dependent forces.

Findings

Successfully learned dynamics of nonlinear physical systems.

Accurately recovered Hamiltonian, forces, and dissipative coefficients.

Predicted trajectories of chaotic systems like the Duffing equation.

Abstract

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known apriori. Despite this success, many real world dynamical systems are non-autonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such non-autonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed \emph{port-Hamiltonian neural network} can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.