Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm
Numerical Analysis
2018-03-06 v2 Mathematical Physics
math.MP
Optimization and Control
Abstract
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 method based on Sinkhorn's algorithm for the entropic regularization of optimal transport. We also make a detailed comparison of this entropic regularization with the so-called Bredinger entropic interpolation problem. Numerical results in dimension one and two illustrate the feasibility of the method.
Cite
@article{arxiv.1710.08234,
title = {Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm},
author = {Jean-David Benamou and Guillaume Carlier and Luca Nenna},
journal= {arXiv preprint arXiv:1710.08234},
year = {2018}
}