Qin Li

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1paper
809citations

1 Paper

5.5MLJun 12, 2024
Forward-Euler time-discretization for Wasserstein gradient flows can be wrong

Yewei Xu, Qin Li

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.