Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernels

arXiv:2301.11624v3 Announce Type: replace
Abstract: Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the understanding of such flows. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot …

abstract arxiv become continuous cs.lg gradient math.oc math.pr mean paper show singular type understanding