Structure- and stability-preserving learning-based model order reduction for port-Hamiltonian systems

This paper addresses the problem of data-driven model order reduction for port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability. We propose a novel approach that, unlike existing methods, does not require the availability of samples of the Hamiltonian and its gradient within the training data. Our method employs a Petrov–Galerkin projection approach and introduces a neural network-based approximation technique designed to learn the Hamiltonian while explicitly preserving equilibrium conditions characterized by the vanishing gradient of the Hamiltonian. Conventional neural network-based Hamiltonian approximations often impose convexity constraints, which can limit the expressiveness and generalization of the learned models. In contrast, our approach relaxes this convexity requirement, enabling the adoption of more general non-convex models to enhance flexibility and performance. A numerical experiment is presented to validate the effectiveness of the proposed method, demonstrating its capability to achieve accurate structure- and stability-preserving order reduction for port-Hamiltonian systems.