Matt Jacobs
University of California, Santa Barbara (UCSB)
Title
Provably higher order accurate schemes for Wasserstein gradient flows
Abstract
In this talk, we study higher-order-accurate-in-time minimizing movements schemes for Wasserstein gradient flows. We introduce a novel accelerated second-order scheme, leveraging the differential structure of the Wasserstein space in both Eulerian and Lagrangian coordinates. For sufficiently smooth solutions, we show that our scheme provably achieves an optimal quadratic convergence rate, which represents the first fully rigorous proof of accelerated rates. Under the weaker assumptions of Wasserstein differentiability and λ-displacement convexity, we show that our scheme still achieves a first-order convergence rate and has strong numerical stability.
