Forward-Euler time-discretization for Wasserstein gradient flows can be wrong
Machine Learning
2024-06-13 v1 Machine Learning
Optimization and Control
Abstract
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.
Cite
@article{arxiv.2406.08209,
title = {Forward-Euler time-discretization for Wasserstein gradient flows can be wrong},
author = {Yewei Xu and Qin Li},
journal= {arXiv preprint arXiv:2406.08209},
year = {2024}
}