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Entropic Optimal Transport Solutions of the Semigeostrophic Equations

Benamou, Jean-David; Cotter, Colin; Malamut, Hugo (2023), Entropic Optimal Transport Solutions of the Semigeostrophic Equations. https://basepub.dauphine.psl.eu/handle/123456789/24492

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Type
Document de travail / Working paper
Date
2023
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
25
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Author(s)
Benamou, Jean-David
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Cotter, Colin
Department of Mathematics [Imperial College London]
Malamut, Hugo
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
The Semigeostrophic equations are a frontogenesis model in atmospheric science. Existence of solutions both from the theoretical and numerical point of view is given under a change of variable involving the interpretation of the pressure gradient as an Optimal Transport map between the density of the fluid and its push forward. Thanks to recent advances in numerical Optimal Transportation, the computation of large scale discrete approximations can be envisioned. We study here the use of Entropic Optimal Transport and its Sinkhorn algorithm companion.