Helmholtz-Hodge
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events
Announce Type: cross Abstract: Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity $u(z)$, whose streamlines trace the dominant reaction pathways, and a scalar potential $h(z)$, obtained from a weighted Helmholtz-Hodge decomposition of the...
Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events
Announce Type: new Abstract: Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity $u(z)$, whose streamlines trace the dominant reaction pathways, and a scalar potential $h(z)$, obtained from a weighted Helmholtz-Hodge decomposition of the...
A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations
arXiv:2605.18250v2 Announce Type: replace-cross Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered, and data-driven systems. This work provides a unified perspective on such systems by connecting continuous formulations based on the Helmholtz-Hodge decomposition with discrete and data-driven...
A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations
arXiv:2605.18250v2 Announce Type: replace Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered, and data-driven systems. This work provides a unified perspective on such systems by connecting continuous formulations based on the Helmholtz-Hodge decomposition with discrete and data-driven representations.
Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors
arXiv:2606.06179v1 Announce Type: cross Abstract: Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the $L^2$ score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large $L^2$ score error while perfectly matching the target...