Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach
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Abstract (arXiv)
Embedding physical intuition into network architectures allows the learning of dynamics that enforce fundamental properties, such as energy conservation laws, thereby leading to physically-plausible predictions. Yet, scaling these models to high-dimensional dynamical systems remains a significant challenge. This paper introduces 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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 27 of its 57 references that are in the map. First posted on arXiv 29 Sep 2025.
Builds on
27 of 57 references.
References · 27
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15 more
- 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 34
- 2020Nonseparable Symplectic Neural Networkscited by 31
- 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
- 2023Harnessing the Power of Neural Operators with Automatically Encoded Conservation Lawscited by 24
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- 2025Riemann Tensor Neural Networks: Learning Conservative Systems with Physics-Constrained Networkscited by 2
- 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
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Citing papers per year: 2026: 2.
2 papers.