Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach

Katharina Friedl, Noémie Jaquier, Alyx Liao, Danica Kragic
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:31637-31668, 2026.

Abstract

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 intrinsically 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-friedl26a, title = {Learning {H}amiltonian Dynamics at Scale: A Differential-Geometric Approach}, author = {Friedl, Katharina and Jaquier, No\'{e}mie and Liao, Alyx and Kragic, Danica}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {31637--31668}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/friedl26a/friedl26a.pdf}, url = {https://proceedings.mlr.press/v306/friedl26a.html}, abstract = {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 intrinsically 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.} }
Endnote
%0 Conference Paper %T Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach %A Katharina Friedl %A Noémie Jaquier %A Alyx Liao %A Danica Kragic %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-friedl26a %I PMLR %P 31637--31668 %U https://proceedings.mlr.press/v306/friedl26a.html %V 306 %X 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 intrinsically 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.
APA
Friedl, K., Jaquier, N., Liao, A. & Kragic, D.. (2026). Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:31637-31668 Available from https://proceedings.mlr.press/v306/friedl26a.html.

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