Controlled oscillation modeling using port-Hamiltonian neural networks

Authors

M. Linares, G. Doras, T. Hélie, A. Roebel

Abstract

Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been successfully applied for modeling mechanical systems. However, even though these methods are designed on power-balance principles, they usually do not consider power-preserving discretizations and often rely on Runge-Kutta numerical methods. In this work, we propose to use a second-order discrete gradient method embedded in the learning of dynamical systems with port-Hamiltonian neural networks. Numerical results are provided for three systems deliberately selected to span different ranges of dynamical behavior under control: a baseline harmonic oscillator with quadratic energy storage; a Duffing oscillator, with a non-quadratic Hamiltonian offering amplitude-dependent effects; and a self-sustained oscillator, which can stabilize in a controlled limit cycle through the incorporation of a nonlinear dissipation. We show how the use of this discrete gradient method outperforms the performance of a Runge-Kutta method of the same order. Experiments are also carried out to compare two theoretically equivalent port-Hamiltonian systems formulations and to analyze the impact of regularizing the Jacobian of port-Hamiltonian neural networks during training.

Keywords

discrete gradient, jacobian regularization, physics-informed machine learning, port-hamiltonian neural networks

Citation

• Journal: Physica D: Nonlinear Phenomena
• Year: 2026
• Volume: 497
• Issue:
• Pages: 135341
• Publisher: Elsevier BV
• DOI: 10.1016/j.physd.2026.135341

BibTeX

@article{Linares_2026,
  title={{Controlled oscillation modeling using port-Hamiltonian neural networks}},
  volume={497},
  ISSN={0167-2789},
  DOI={10.1016/j.physd.2026.135341},
  journal={Physica D: Nonlinear Phenomena},
  publisher={Elsevier BV},
  author={Linares, M. and Doras, G. and Hélie, T. and Roebel, A.},
  year={2026},
  pages={135341}
}

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