# Identifying the nonlinear string dynamics with port-Hamiltonian neural networks

arXiv: https://arxiv.org/abs/2605.12785 · HTML: https://mlsanity.com/paper/2605.12785/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 14 of 14)

- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Stable Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2502.02480/) (2025)
- [Physical Modeling using Recurrent Neural Networks with Fast Convolutional Layers](https://mlsanity.com/paper/2204.10125/) (2022)
- [Pseudo-Hamiltonian neural networks for learning partial differential equations](https://mlsanity.com/paper/2304.14374/) (2023)
- [Nonlinear port-Hamiltonian system identification from input-state-output data (ISO-pHNN)](https://mlsanity.com/paper/2501.06118/) (2025)
- [Differentiable Modal Synthesis for Physical Modeling of Planar String Sound and Motion Simulation](https://mlsanity.com/paper/2407.05516/) (2024)
- [Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods](https://mlsanity.com/paper/2408.16650/) (2024)
- [Port-Hamiltonian Neural Networks with Output Error Noise Models](https://mlsanity.com/paper/2502.14432/) (2025)
- [Fast Differentiable Modal Simulation of Non-linear Strings, Membranes, and Plates](https://mlsanity.com/paper/2505.05940/) (2025)
- [Physics-Informed Deep Learning for Nonlinear Friction Model of Bow-string Interaction](https://mlsanity.com/paper/2505.18950/) (2025)
- [Predictions Based on Pixel Data: Insights from PDEs and Finite Differences](https://mlsanity.com/paper/2305.00723/) (2023)
- [Learning Nonlinear Dynamics in Physical Modelling Synthesis using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2505.10511/) (2025)
- [Controlled oscillation modeling using port-Hamiltonian neural networks](https://mlsanity.com/paper/2602.15704/) (2026)
- [PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network](https://mlsanity.com/paper/2606.14708/) (2026)

## Abstract (arXiv)

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.