Saved in:
Bibliographic Details
Main Authors: Xu, Yewei, Li, Qin
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.08209
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911914377871360
author Xu, Yewei
Li, Qin
author_facet Xu, Yewei
Li, Qin
contents In this note, we examine the forward-Euler discretization for simulating Wasserstein gradient flows. We provide two counter-examples showcasing the failure of this discretization even for a simple case where the energy functional is defined as the KL divergence against some nicely structured probability densities. A simple explanation of this failure is also discussed.
format Preprint
id arxiv_https___arxiv_org_abs_2406_08209
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Forward-Euler time-discretization for Wasserstein gradient flows can be wrong
Xu, Yewei
Li, Qin
Machine Learning
Optimization and Control
65M12
In this note, we examine the forward-Euler discretization for simulating Wasserstein gradient flows. We provide two counter-examples showcasing the failure of this discretization even for a simple case where the energy functional is defined as the KL divergence against some nicely structured probability densities. A simple explanation of this failure is also discussed.
title Forward-Euler time-discretization for Wasserstein gradient flows can be wrong
topic Machine Learning
Optimization and Control
65M12
url https://arxiv.org/abs/2406.08209