Entropic optimal transport solutions of the semigeostrophic equations

I will present an algorithm for solving the semigeostrophic approximation of the vertical slice Eady equations, a simplified atmosphere model that exhibits frontogenesis. The algorithm follows the weak Lagrangian optimal transport formulation of the semigeostrophic equations, which poses the transformation to geostrophic coordinates as the solution to an optimal transport problem. To obtain an efficient numerical solution we add an entropic regularisation to the optimal transport problem, and approximate the density in both physical and geostrophic coordinates by a set of Dirac masses. The optimal transport problem can then be solved using the Sinkhorn algorithm, which can be accelerated by a multiscale approach. In the talk I will attempt to explain the optimal transport formulation before describing the algorithm and presenting some numerical results.
Benamou, Jean-David., Colin Cotter, and Hugo Malamut. "Entropic Optimal Transport Solutions of the Semigeostrophic Equations." Journal of Computational Physics (2024): 112745.