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

Authors

Shaan A. Desai, Marios Mattheakis, David Sondak, Pavlos Protopapas, Stephen J. Roberts

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 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.

Citation

• Journal: Physical Review E
• Year: 2021
• Volume: 104
• Issue: 3
• Pages:
• Publisher: American Physical Society (APS)
• DOI: 10.1103/physreve.104.034312

BibTeX

@article{Desai_2021,
  title={{Port-Hamiltonian neural networks for learning explicit time-dependent dynamical systems}},
  volume={104},
  ISSN={2470-0053},
  DOI={10.1103/physreve.104.034312},
  number={3},
  journal={Physical Review E},
  publisher={American Physical Society (APS)},
  author={Desai, Shaan A. and Mattheakis, Marios and Sondak, David and Protopapas, Pavlos and Roberts, Stephen J.},
  year={2021}
}

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