The back-and-forth method for Wasserstein gradient flows

We present a method to efficiently compute Wasserstein gradient flows. Our approach is based on a generalization of the back-and-forth method (BFM) introduced in Jacobs and Léger [ Numer. Math. 146 (2020) 513–544.]. to solve optimal transport problems. We evolve the gradient flow by solving the dual...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 27; p. 28
Main Authors Jacobs, Matt, Lee, Wonjun, Léger, Flavien
Format Journal Article
LanguageEnglish
Published 2021
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Summary:We present a method to efficiently compute Wasserstein gradient flows. Our approach is based on a generalization of the back-and-forth method (BFM) introduced in Jacobs and Léger [ Numer. Math. 146 (2020) 513–544.]. to solve optimal transport problems. We evolve the gradient flow by solving the dual problem to the JKO scheme. In general, the dual problem is much better behaved than the primal problem. This allows us to efficiently run large scale gradient flows simulations for a large class of internal energies including singular and non-convex energies.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2021029