Calculus of Variations and Geometric Measure Theory
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J. D. Benamou - G. Carlier - L. Nenna

Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm

created by nenna on 23 Oct 2017
modified on 24 Oct 2017

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Submitted Paper

Inserted: 23 oct 2017
Last Updated: 24 oct 2017

Year: 2017

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 (see 1). Numerical results in dimension one and two illustrate the feasibility of the method.


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