{"ID":2863514,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.24627","arxiv_id":"2509.24627","title":"Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach","abstract":"By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a significant challenge. This paper introduces Geometric Reduced-order Hamiltonian Neural Network (RO-HNN), a novel physics-inspired neural network that combines the conservation laws of Hamiltonian mechanics with the scalability of model order reduction. RO-HNN is built on two core components: a novel geometrically-constrained symplectic autoencoder that learns a low-dimensional, structure-preserving symplectic submanifold, and a geometric Hamiltonian neural network that models the dynamics on the submanifold. Our experiments demonstrate that RO-HNN provides physically-consistent, stable, and generalizable predictions of complex high-dimensional dynamics, thereby effectively extending the scope of Hamiltonian neural networks to high-dimensional physical systems.","short_abstract":"By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a significant challenge. This paper introduces Geometric Reduced-order Hamiltonian Neural...","url_abs":"https://arxiv.org/abs/2509.24627","url_pdf":"https://arxiv.org/pdf/2509.24627v1","authors":"[\"Katharina Friedl\",\"Noémie Jaquier\",\"Alyx Liao\",\"Danica Kragic\"]","published":"2025-09-29T11:36:35Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}