Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm

Abstract : Starting from Brenier's relaxed formulation of the incompress-ible 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 regular-ization 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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Jean-David Benamou, Guillaume Carlier, Luca Nenna. Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm. 2018. ⟨hal-01621311v2⟩

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