Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm
Provides a new computational approach for incompressible flows, but the results are preliminary and limited to low dimensions.
The authors propose a numerical method based on the Sinkhorn algorithm for solving generalized incompressible flow problems using entropic regularization of optimal transport, demonstrating feasibility in 1D and 2D.
Starting from Brenier's relaxed formulation of the incompressible 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 regularization with the so-called Bredinger entropic interpolation problem. Numerical results in dimension one and two illustrate the feasibility of the method.