Forward-Euler time-discretization for Wasserstein gradient flows can be wrong

Yewei Xu, Qin Li
6/12/2024
stat.MLcs.LGmath.OC

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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.

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Cite this paper

@article{xu2024forwardeuler,
  title  = {Forward-Euler time-discretization for Wasserstein gradient flows can be wrong},
  author = {Yewei Xu and Qin Li},
  year   = {2024},
  eprint = {2406.08209},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2406.08209v1}
}

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