Port-Hamiltonian neural networks for learning explicit time-dependent dynamical systems

Journal article

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 a priori. Despite this success, many real world dynamical systems are nonautonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such nonautonomous 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 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.

Authors: Desai, SA; Mattheakis, M; Sondak, D; Protopapas, P; Roberts, SJ

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review E
• Volume: 104
• Issue: 3
• Article number: 034312
• Place of publication: United States
• Publication date: 2021-09-29
• Acceptance date: 2021-09-14
• DOI: 10.1103/physreve.104.034312
• EISSN: 2470-0053
• ISSN: 2470-0045
• Pmid: 34654178
• Language: English
• Keywords: FFR