Particle flow and Monge-Kantorovich transport

We compare our new particle flow nonlinear filter algorithms with Monge-Kantorovich optimal transport (MKT) algorithms. These two classes of algorithms are the same in several ways, but they differ in computational complexity and the overall intended purpose, as well as differing in several crucial details of the computation and the problem. Moreover, the deep mathematical theory of incompressible particle flow that was developed recently by Shnirelman can be used to provide insight into why our particle flow algorithms work so well.