Sujet: Optimal transport, Euler equations,
نویسندگان
چکیده
منابع مشابه
Variational Particle Schemes for the Porous Medium Equation and for the System of Isentropic Euler Equations
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they c...
متن کاملOptimal Transport for the System of Isentropic Euler Equations
We introduce a new variational time discretization for the system of isentropic Euler equations. In each timestep the internal energy is reduced as much as possible, subject to a constraint imposed by a new cost functional that measures the deviation of particles from their characteristic paths.
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The system of isentropic Euler equations in the potential flow regime can be considered formally as a second order ordinary differential equation on the Wasserstein space of probability measures. This interpretation can be used to derive a variational time discretization. We prove that the approximate solutions generated by this discretization converge to a measure-valued solution of the isentr...
متن کاملLeast Action Principles for Incompressible Flows and Optimal Transport between Shapes
As V. I. Arnold observed in the 1960s, the Euler equations of incompressible fluid flow correspond formally to geodesic equations in a group of volume-preserving diffeomorphisms. Working in an Eulerian framework, we study incompressible flows of shapes as critical paths for action (kinetic energy) along transport paths constrained to be shape densities (characteristic functions). The formal geo...
متن کاملIterative Bregman Projections for Regularized Transportation Problems
This article details a general numerical framework to approximate solutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized problem corresponds to a Kullback-Leibler Bregman divergence projection of a vector (representing some initial joint distribution) on the polytope of constraints. W...
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