Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach

• URL: http://arxiv.org/abs/2509.24627v1
• Date: Mon, 29 Sep 2025 11:36:35 GMT
• Title: Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach
• Authors: Katharina Friedl, Noémie Jaquier, Mika Liao, Danica Kragic,
• Abstract summary: This paper introduces a novel physics-inspired neural network that combines the conservation laws of Hamiltonian mechanics with the scalability of model order reduction.<n>Our experiments demonstrate that RO-HNN provides physically-consistent, stable, and generalizable predictions of complex high-dimensional dynamics.
• Score: 15.500592651570384
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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