arXiv Machine Learning June 2, 2026 By Katharina Friedl, No\'emie Jaquier, Alyx Liao, Danica Kragic

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach

Read the original on arXiv Machine Learning →

arXiv:2509. 24627v2 Announce Type: replace 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.

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arXiv Machine Learning

Jun 4

Learning symplectic model reduction based on a approximation theorem of symplectic embeddings

arXiv:2606. 04623v1 Announce Type: new Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics evolving on symplectic manifolds.

By Liyi Feng, Yifa Tang, Yulin Xie, Ruili Zhang, Aiqing Zhu

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arXiv Machine Learning

Aug 18

Learning symplectic model reduction based on an approximation theorem of symplectic embeddings

arXiv:2606. 04623v2 Announce Type: replace Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics that evolve on symplectic manifolds.

By Liyi Feng, Yifa Tang, Yulin Xie, Ruili Zhang, Aiqing Zhu

rag

arXiv Machine Learning

Jun 26

Symplectic Neural Networks for learning Generalized Hamiltonians

arXiv:2606. 27029v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.

By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas

arXiv Machine Learning

Aug 5

Symplectic Neural Networks for Learning Non-Separable Hamiltonians

arXiv:2606. 27029v2 Announce Type: replace Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.

By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas

arXiv Machine Learning

Aug 4

CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamics

arXiv:2608. 00571v1 Announce Type: new Abstract: Learning solution operators for differential equations is a central problem in scientific machine learning.

By Baige Xu, Takaharu Yaguchi

arXiv Machine Learning

Jul 10

Neural non-canonical Hamiltonian dynamics for long-time simulations

arXiv:2510. 01788v2 Announce Type: replace Abstract: This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes.

By Cl\'ementine Court\`es (IRMA, MACARON), Emmanuel Franck (MACARON), Michael Kraus (IPP), Laurent Navoret (IRMA, MACARON), L\'eopold Tr\'emant (LML)

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Learning symplectic model reduction based on a approximation theorem of symplectic embeddings

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