A JKO Splitting Scheme for Kantorovich--Fisher--Rao Gradient Flows

A JKO Splitting Scheme for Kantorovich-Fisher-Rao Gradient Flows

In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting som...

Gradient Flows in Filtering and Fisher-Rao Geometry

Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and a systematic way to formulate and solve the same for linear Gaussian systems has appeared in our previous work where the gradient flows were realized via pr...

The Wasserstein-Fisher-Rao metric

This note gives a summary of the presentation that I gave at the workshop on shape analysis. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to measures that have different total masses. This generalization enjoys most of the properties of standard optimal transport but we will focus on the geometric formulation of the model. We expect this new metric to have interes...

Minimizing Flows for the Monge-Kantorovich Problem

Simulation of Multiphase Flows Using a Modified Upwind-Splitting Scheme

A robust AUSM upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of ...