Controlled oscillation modeling using port-Hamiltonian neural networks

• URL: http://arxiv.org/abs/2602.15704v1
• Date: Tue, 17 Feb 2026 16:38:41 GMT
• Title: Controlled oscillation modeling using port-Hamiltonian neural networks
• Authors: Maximino Linares, Guillaume Doras, Thomas Hélie,
• Abstract summary: We propose a second-order discrete gradient method embedded in the learning of dynamical systems with port-Hamiltonian neural networks.<n>We show how the use of this discrete gradient method outperforms the performance of a Runge-Kutta method of the same order.
• Score: 0.30586855806896035
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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