50 citations · 153 across the 32 of their papers we have counts for
3 papers · 1 filter
Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm
Jean-David Benamou, Guillaume Carlier, Luca Nenna
Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of geodesics in the group of measure-preserving diffeomorphisms, we propose a numerical me…
Deep Relaxation: partial differential equations for optimizing deep neural networks
Pratik Chaudhari, Adam Oberman, Stanley Osher +2
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation te…
On the total variation Wasserstein gradient flow and the TV-JKO scheme
Guillaume Carlier, Clarice Poon
We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a form of maximum principle and in some case…