arXiv subjects

Thomas Hélie

Publications and source records attributed to Thomas Hélie.

3 recordsLinked to original sources

arXiv2026

Identifying the nonlinear string dynamics with port-Hamiltonian neural networks

Hybrid machine learning combines physical knowledge with data-driven models to enhance interpretability and performance. In this context, Port-Hamiltonian Systems (PHS), which generalize Hamiltonian mechanics to describe open, non-autonomous dynamical systems, have been successfully integrated with neural networks under the name Port-Hamiltonian Neural Networks (PHNNs). While the ability of PHNNs to identify Hamiltonian ordinary differential equation (ODE) systems has already been demonstrated, their application to learning Hamiltonian partial differential equation (PDE) systems remains largely unexplored. This limitation restricts their use in musical acoustics, where instruments are typically modeled as distributed parameter systems governed by PDEs. In this work, we demonstrate how to learn the nonlinear string dynamics from data in a physically-consistent framework through a PHNN extension to PDEs. By constructing structured neural network architectures based on PHS, we can recover both the Hamiltonian governing the string and the dissipation affecting it. This approach outperforms baseline, non-physics-informed methods in terms of both accuracy and interpretability. Numerical experiments using synthetic data demonstrate the ability of the proposed PHNN model to identify and emulate the nonlinear dynamics of the system.

cs.LG↗

arXiv2026

Controlled oscillation modeling using port-Hamiltonian neural networks

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.

cs.LG↗

arXiv2023

From equilibrium statistical physics under experimental constraints to macroscopic port-Hamiltonian systems

This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The environment, assumed to be slow, is modeled through experimental constraints on macroscopic quantities (e.g. energy, particle number, etc), with a partitioning into two classes: non fluctuating and fluctuating values. The method to derive the PH macroscopic laws is detailed in several steps and illustrated on two standard cases (ideal gas, Ising ferromagnets). It revisits equilibrium statistical physics with a focus on this partitioning. First, the Boltzmann's principle is used to provide the statistic law of the matter. It defines a macroscopic equilibrium characterized by a scalar value, the entropy, together with thermodynamic quantities emerging from each constraint. Then, the port-Hamiltonian system is derived. The Hamiltonian (macroscopic energy) is derived as a function of the macroscopic state (entropy and the macroscopic quantities associated with the fluctuating class). The ports (flows/efforts) are related to the time-derivative of the state and the Hamiltonian gradient in a conservative way. This open system defines the reversible laws that govern standard thermodynamic quantities. Lastly, this paper presents a strategy to extend this PH system to an irreversible conservative one, given a macroscopic dissipative law.

math.DS↗