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Optimal transport methods have recently established state of the art accuracy and efficiency for holographic laser beam shaping. However, use of such methods is hindered by severe $\mathcal{O}(N^2)$ memory and $\mathcal{O}(N^2)$ time…

Optics · Physics 2026-02-23 Andrii Torchylo , Hunter Swan , Lucas Tellez , Jason M. Hogan

The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…

Machine Learning · Statistics 2025-12-11 Sloan Nietert , Ziv Goldfeld

Although vital to computer vision systems, few-shot action recognition is still not mature despite the wide research of few-shot image classification. Popular few-shot learning algorithms extract a transferable embedding from seen classes…

Computer Vision and Pattern Recognition · Computer Science 2021-04-09 Su Lu , Han-Jia Ye , De-Chuan Zhan

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…

Optimization and Control · Mathematics 2020-10-23 Luca De Gennaro Aquino , Stephan Eckstein

Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large pile of sand lying on a construction site. The goal of the…

Machine Learning · Statistics 2020-03-20 Gabriel Peyré , Marco Cuturi

In this paper, we address the numerical solution to the multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including…

Optimization and Control · Mathematics 2023-07-21 Bohan Zhou , Matthew Parno

Optimal deployment and movement of multiple unmanned aerial vehicles (UAVs) is studied. The considered scenario consists of several ground terminals (GTs) communicating with the UAVs using variable transmission power and fixed data rate.…

Information Theory · Computer Science 2018-11-29 Erdem Koyuncu , Maryam Shabanighazikelayeh , Hulya Seferoglu

We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…

Computer Vision and Pattern Recognition · Computer Science 2016-10-06 Nicolas Papadakis , Julien Rabin

Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…

Machine Learning · Computer Science 2025-05-20 Peter Chen , Yue Xie , Qingpeng Zhang

Whilst optimal transport (OT) is increasingly being recognized as a powerful and flexible approach for dealing with fairness issues, current OT fairness methods are confined to the use of discrete OT. In this paper, we leverage recent…

Machine Learning · Computer Science 2021-01-07 Silvia Chiappa , Aldo Pacchiano

In this work, we propose a framework to store and manage spatial data, which includes new efficient algorithms to perform operations accepting as input a raster dataset and a vector dataset. More concretely, we present algorithms for…

Data Structures and Algorithms · Computer Science 2020-04-07 Fernando Silva-Coira , José R. Paramá , Susana Ladra , Juan R. López , Gilberto Gutiérrez

Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…

Machine Learning · Computer Science 2026-03-05 Henri Schmidt , Peter Halmos , Ben Raphael

Alignment plays a fundamental role in many machine learning problems, such as multi-network analysis, multimodal learning, and point cloud registration. Recent works increasingly leverage optimal transport (OT) for distributional alignment,…

Machine Learning · Computer Science 2026-05-26 Qi Yu , Ruizhong Qiu , Zhichen Zeng , My T. Thai , Huan Liu , Hanghang Tong

We investigate a matrix dynamical system related to optimal mass transport in the linear category, namely, the problem of finding an optimal invertible matrix by which two covariance matrices are congruent. We first review the differential…

Optimization and Control · Mathematics 2024-11-27 Erik Jansson , Klas Modin

Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…

Machine Learning · Statistics 2018-03-06 Brahim Khalil Abid , Robert M. Gower

We provide a survey of recent results on model calibration by Optimal Transport. We present the general framework and then discuss the calibration of local, and local-stochastic, volatility models to European options, the joint VIX/SPX…

Mathematical Finance · Quantitative Finance 2021-07-06 Ivan Guo , Gregoire Loeper , Jan Obloj , Shiyi Wang

The goal of Optimal Transmission Switching (OTS) problem for power systems is to identify a topology of the power grid that minimizes the cost of the system operation while satisfying the operational and physical constraints. Among the most…

Optimization and Control · Mathematics 2021-10-18 Juncheng Li , Trivikram Dokka , Guglielmo Lulli , Fabrizio Lacalandra

The volumetric stretch energy has been widely applied to the computation of volume-/mass-preserving parameterizations of simply connected tetrahedral mesh models. However, this approach still lacks theoretical support. In this paper, we…

Numerical Analysis · Mathematics 2022-10-19 Tsung-Ming Huang , Wei-Hung Liao , Wen-Wei Lin , Mei-Heng Yueh , Shing-Tung Yau

Motivated by applications in classification of vector valued measures and multispecies PDE, we develop a theory that unifies existing notions of vector valued optimal transport, from dynamic formulations (\`a la Benamou-Brenier) to static…

Analysis of PDEs · Mathematics 2025-05-07 Katy Craig , Nicolás García Trillos , Đorđe Nikolić

Recently, Papadakis et al. proposed an efficient primal-dual algorithm for solving the dynamic optimal transport problem with quadratic ground cost and measures having densities with respect to the Lebesgue measure. It is based on the fluid…

Numerical Analysis · Mathematics 2015-09-02 Jan Henrik Fitschen , Friederike Laus , Gabriele Steidl