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Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm

Benamou, Jean-David; Carlier, Guillaume; Nenna, Luca (2019), Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm, Numerische Mathematik, 142, p. 33–54. 10.1007/s00211-018-0995-x

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Numerische Mathematik
Volume
142
Publisher
Springer
Pages
33–54
Publication identifier
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Author(s)
Benamou, Jean-David
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Nenna, Luca
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Generalized incompressible flows; Incompressible Euler equations; Sinkhorn algorithm; Entropic regularization; Multi-marginal optimal transport