# Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems

arXiv: https://arxiv.org/abs/2604.13297 · HTML: https://mlsanity.com/paper/2604.13297/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces](https://mlsanity.com/paper/2206.02660/) (2022)
- [Stable Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2502.02480/) (2025)
- [Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Control](https://mlsanity.com/paper/2401.09520/) (2024)
- [Nonlinear port-Hamiltonian system identification from input-state-output data (ISO-pHNN)](https://mlsanity.com/paper/2501.06118/) (2025)
- [Data-driven identification of latent port-Hamiltonian systems](https://mlsanity.com/paper/2408.08185/) (2024)
- [Discrete-time port-Hamiltonian systems: A definition based on symplectic integration](https://mlsanity.com/paper/1811.07852/) (2018)
- [Adaptive Sampling for Structure Preserving Model Order Reduction of Port-Hamiltonian Systems](https://mlsanity.com/paper/2106.11366/) (2021)
- [Hamiltonian Dynamics Learning from Point Cloud Observations for Nonholonomic Mobile Robot Control](https://mlsanity.com/paper/2309.09163/) (2023)
- [Robust Neural IDA-PBC: passivity-based stabilization under approximations](https://mlsanity.com/paper/2409.16008/) (2024)

## Abstract (arXiv)

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling technique that relaxes the convexity constraint commonly imposed by neural network-based Hamiltonian approximations, thereby improving the expressiveness and generalization capability of the model. By removing this restriction, the proposed approach enables the use of more general non-convex Hamiltonian representations to enhance modeling flexibility and accuracy. Furthermore, the proposed method incorporates information about stable equilibria into the learning process, allowing the learned model to preserve the stability of multiple isolated equilibria rather than being restricted to a single equilibrium as in conventional methods. Two numerical experiments are conducted to validate the effectiveness of the proposed approach and demonstrate its ability to achieve more accurate structure- and stability-preserving learning of port-Hamiltonian systems compared with a baseline method.