Related papers: Entropy-minimizing dynamical transport on Riemanni…

We prove existence and uniqueness results for solutions to a class of optimal transportation problems with infinitely many marginals, supported on the real line. We also provide a characterization of the solution with an explicit formula.…

We obtain an explicit solution for the static Kullback--Leibler (KL) unbalanced optimal transport problem between finite non-degenerate Gaussian measures with quadratic cost, two independent positive marginal relaxation parameters, and no…

Entropic optimal transport (EOT) presents an effective and computationally viable alternative to unregularized optimal transport (OT), offering diverse applications for large-scale data analysis. In this work, we derive novel statistical…

In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…

In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…

We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the…

We prove that if $\Omega\subset \mathbb{R}^{n+1}$ is a (not necessarily strictly) convex, $C^1$ domain, and $\mu$ and $\bar{\mu}$ are probability measures absolutely continuous with respect to surface measure on $\partial \Omega$, with…

Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geometry can distort distances, averages, and the resulting…

Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…

We show that the discrete Sinkhorn algorithm - as applied in the setting of Optimal Transport on a compact manifold - converges to the solution of a fully non-linear parabolic PDE of Monge-Ampere type, in a large-scale limit. The latter…

We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…

In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…

In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…

Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…

Given a metric measure space $(X,\mathsf{d},\mathfrak{m})$ and a lower semicontinuous, lower bounded function $k\colon X\to\mathbb{R}$, we prove the equivalence of the synthetic approaches to Ricci curvature at $x\in X$ being bounded from…

Robotic motion optimization often focuses on task-specific solutions, overlooking fundamental motion principles. Building on Riemannian geometry and the calculus of variations (often appearing as indirect methods of optimal control), we…

Entropic optimal transport -- the optimal transport problem regularized by KL diver\-gence -- is highly successful in statistical applications. Thanks to the smoothness of the entropic coupling, its sample complexity avoids the curse of…

We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…

The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by…

Let $(X,d,m)$ be a proper, non-branching, metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex functions of the distance, provided $(X,d,m)$ satisfies a new…