The back-and-forth method for Wasserstein gradient flows

¹ UCLA, Los Angeles, CA, USA.
² ENS, PSL University, Paris, France.

^* Corresponding author: majaco@math.ucla.edu

Received: 17 November 2020
Accepted: 9 March 2021

Abstract

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.