Volume 27, 2021
|Number of page(s)||35|
|Published online||30 March 2021|
The back-and-forth method for Wasserstein gradient flows
2 ENS, PSL University, Paris, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 9 March 2021
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.
Mathematics Subject Classification: 65K10 / 65N99 / 49N15 / 90C46
Key words: Optimal transport / Wasserstein gradient flows / JKO scheme / back-and-forth method / Porous media equation / Crowd motion models / Numerical optimization
© EDP Sciences, SMAI 2021
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