113 citations · 638 across the 37 of their papers we have counts for
4 papers · 1 filter
Quantum Optimal Transport for Tensor Field Processing
Gabriel Peyré, Lenaïc Chizat, François-Xavier Vialard +1
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formu…
The Camassa-Holm equation as an incompressible Euler equation: a geometric point of view
Thomas Gallouët, François-Xavier Vialard
The group of diffeomorphisms of a compact manifold endowed with the L^2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler…
Scaling Algorithms for Unbalanced Transport Problems
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer +1
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only…
Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric
Rabah Tahraoui, François-Xavier Vialard
We study a second-order variational problem on the group of diffeomorphisms of the interval [0, 1] endowed with a right-invariant Sobolev metric of order 2, which consists in the m…