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.
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: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.
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.
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.
arXiv:2608. 00571v1 Announce Type: new Abstract: Learning solution operators for differential equations is a central problem in scientific machine learning.
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.
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:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.
arXiv:2607. 28939v1 Announce Type: new Abstract: Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data.
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.
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.
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.