Identifying the nonlinear string dynamics with port-Hamiltonian neural networks

TL;DR

This paper extends port-Hamiltonian neural networks to learn nonlinear string dynamics described by PDEs, improving accuracy and interpretability in modeling distributed parameter systems like musical instruments.

Contribution

The work introduces a PHNN extension for PDEs, enabling physically-consistent learning of nonlinear string dynamics from data, which was previously unexplored.

Findings

Outperforms baseline methods in accuracy and interpretability

Successfully identifies Hamiltonian and dissipation in string dynamics

Demonstrates effectiveness on synthetic data for nonlinear PDE systems

Abstract

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.