Title: Scalable Learning of Hamiltonian Dynamics via Differential Geometry

Abstract: Integrating physical priors into neural network architectures enables the modeling of dynamics that adhere to fundamental principles, such as energy conservation, resulting in predictions that are physically plausible. However, applying these models to high-dimensional dynamical systems continues to pose a substantial challenge. To address this, we present the Reduced-order Hamiltonian Neural Network (RO-HNN), a new physics-inspired architecture that merges the conservation laws inherent in Hamiltonian mechanics with the computational efficiency of model order reduction. The RO-HNN framework relies on two primary elements: a novel symplectic autoencoder constrained by geometric principles, which identifies a low-dimensional, structure-preserving symplectic submanifold, and a geometric Hamiltonian neural network that captures the system's dynamics within this submanifold. Experimental results indicate that RO-HNN delivers stable, generalizable, and physically consistent forecasts for complex high-dimensional systems, significantly broadening the applicability of Hamiltonian neural networks to large-scale physical phenomena.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC