An entropy-regularized, Sinkhorn-based optimal transport discretization of the semigeostrophic shallow water equations is proposed, with a debiasing correction and numerical evidence of convergence.
Well-posedness and convergence of entropic approximation of semi-geostrophic equations
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abstract
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is also proved for discretizations that can be computed numerically in practice as shown recently in [6].
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Entropic approximations of the semigeostrophic shallow water equations
An entropy-regularized, Sinkhorn-based optimal transport discretization of the semigeostrophic shallow water equations is proposed, with a debiasing correction and numerical evidence of convergence.