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

2026-04-14

AI Summary

This work addresses the challenge in data-driven modeling of port-Hamiltonian systems, where preserving structural properties and ensuring stability at multiple equilibria are often difficult to achieve simultaneously. The authors propose a novel neural network approach that explicitly embeds Hamiltonian structure and multi-equilibrium stability constraints into the learning process. By circumventing conventional convexity restrictions, the method enables flexible approximation of non-convex Hamiltonian functions. Through a structure-aware learning framework, it concurrently preserves the system’s intrinsic geometric characteristics and guarantees asymptotic stability at multiple isolated equilibria. Experimental results demonstrate that, compared to existing baselines, the proposed method significantly improves both model accuracy and fidelity in stability preservation across two numerical benchmarks.

Technology Category

• Machine Learning: Structured Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• port-Hamiltonian systems
• structure-preserving learning
• stability preservation
• data-driven modeling
• Hamiltonian structure

Innovation

• port-Hamiltonian systems
• structure-preserving learning
• non-convex Hamiltonian
• stability preservation
• neural network modeling