Entropic Optimal Transport Solutions of the Semigeostrophic Equations

Jean-David Benamou (1) , Colin Cotter (2) , Hugo Malamut (1)

1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
2 Imperial College London

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.

Domaines: Mathématiques [math]

Jean-David Benamou, Colin Cotter, Hugo Malamut. Entropic Optimal Transport Solutions of the Semigeostrophic Equations. 2023. ⟨hal-03960859⟩