scholarly journals {Euclidean, metric, and Wasserstein} gradient flows: an overview

2017 ◽  
Vol 7 (1) ◽  
pp. 87-154 ◽  
Author(s):  
Filippo Santambrogio
Keyword(s):  
Gradient Flows ◽  
Euclidean Metric ◽  
Wasserstein Gradient Flows

scholarly journals Wasserstein gradient flows from large deviations of many-particle limits

2013 ◽  
Vol 19 (4) ◽  
pp. 1166-1188 ◽  
Author(s):  
Manh Hong Duong ◽  
Vaios Laschos ◽  
Michiel Renger
Keyword(s):  
Large Deviations ◽  
Gradient Flows ◽  
Wasserstein Gradient Flows

scholarly journals The back-and-forth method for Wasserstein gradient flows

2021 ◽  
Vol 27 ◽  
pp. 28
Author(s):  
Matt Jacobs ◽  
Wonjun Lee ◽  
Flavien Léger
Keyword(s):  
Large Class ◽  
Large Scale ◽  
Dual Problem ◽  
Optimal Transport ◽  
Gradient Flow ◽  
Gradient Flows ◽  
Primal Problem ◽  
Transport Problems ◽  
Wasserstein Gradient Flows ◽  
Numer Math

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.

scholarly journals A variational finite volume scheme for Wasserstein gradient flows

2020 ◽  
Vol 146 (3) ◽  
pp. 437-480
Author(s):  
Clément Cancès ◽  
Thomas O. Gallouët ◽  
Gabriele Todeschi
Keyword(s):  
Finite Volume ◽  
Finite Volume Scheme ◽  
Gradient Flows ◽  
Volume Scheme ◽  
Wasserstein Gradient Flows
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