arXiv Machine Learning

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.

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

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

rag

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 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

Aug 3

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.

By Robert Simon Fong, Gouhei Tanaka, Kazuyuki Aihara

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

llms robotics

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)

safety

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 17

Geodesic Calculus on Implicitly Defined Latent Manifolds

arXiv:2510. 09468v3 Announce Type: replace Abstract: Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective.

By Florine Hartwig, Josua Sassen, Juliane Braunsmann, Martin Rumpf, Benedikt Wirth

diffusion

arXiv Machine Learning

Jun 17

Variational autoencoders with latent high-dimensional steady geometric flows for dynamics

arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.

By Andrew Gracyk

diffusion

arXiv Machine Learning

Jun 4

Geometry-Preserving Encoder/Decoder in Latent Generative Models

arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.

By Wonjun Lee, Riley C. W. O'Neill, Dongmian Zou, Jeff Calder, Gilad Lerman

diffusion benchmarks

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