arXiv Machine Learning

Symplectic Representation of Legendre Dynamics

arXiv:2512. 19409v2 Announce Type: replace Abstract: Modern learning systems act on internal representations of data, yet how these representations encode underlying physical or statistical structure is often left implicit.

arXiv Machine Learning

1d ago

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 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

rag

arXiv Machine Learning

Jul 9

CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts

arXiv:2607. 06824v1 Announce Type: cross Abstract: Physics-informed learning promises data-efficient and stable dynamics prediction, yet its strongest geometric guarantees have largely remained confined to closed conservative systems.

By Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares, Ioannis Havoutis, Gerard J. Milburn

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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

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 3

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics

arXiv:2607. 28939v1 Announce Type: new Abstract: Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data.

By Vakhtang Putkaradze

arXiv Machine Learning

Jun 25

When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models

arXiv:2606. 24945v1 Announce Type: new Abstract: We ask a representation-learning question about physical world models: when does a conservation law remain certifiable after a model learns a latent representation?

By Hongbo Wang

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arXiv Machine Learning

Jul 7

CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems

arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.

By Jiale Gong (School of Mathematics), Pengzhan Jin (National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China), Dongyang Kuang (School of Mathematics), Lu Li (School of Mathematics), Yifa Tang (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

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arXiv Machine Learning

Jul 7

Statistically Meaningful Geometry (SMG) Beyond the Euclidean Paradigm, with Application to Generative AI

arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.

By Bing Cheng, Yi-Shuai Niu, Howell Tong, Shing-Tung Yau

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arXiv Machine Learning

Jun 2

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach

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.

By Katharina Friedl, No\'emie Jaquier, Alyx Liao, Danica Kragic

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arXiv Machine Learning

Jun 9

GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators

arXiv:2606. 08343v1 Announce Type: new Abstract: We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space.

By Jason Sulskis, Sathya Ravi

rag

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

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