English
Related papers

Related papers: Solving Semi-Discrete Optimal Transport Problems: …

200 papers

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…

Computational Physics · Physics 2024-06-21 Barry Ganapol

Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…

Probability · Mathematics 2023-04-26 Stephan Eckstein , Gudmund Pammer

Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…

Machine Learning · Statistics 2025-10-15 Khai Nguyen

Salient object detection (SOD) aims to segment visually prominent regions in images and serves as a foundational task for various computer vision applications. We posit that SOD can now reach near-supervised accuracy without a single…

Computer Vision and Pattern Recognition · Computer Science 2025-10-21 Muhammad Umer Ramzan , Ali Zia , Abdelwahed Khamis , Noman Ali , Usman Ali , Wei Xiang

Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…

Numerical Analysis · Mathematics 2025-01-13 Moaad Khamlich , Federico Pichi , Gianluigi Rozza

In this paper we are interested in the numerical solution of stochastic differential equations with non negative solutions. Our goal is to construct explicit numerical schemes that preserve positivity, even for super linear stochastic…

Numerical Analysis · Mathematics 2014-12-18 Nikolaos Halidias , Ioannis S. Stamatiou

The Quickest Transshipment Problem is to route flow as quickly as possible from sources with supplies to sinks with demands in a network with capacities and transit times on the arcs. It is of fundamental importance for numerous…

Data Structures and Algorithms · Computer Science 2021-08-16 Miriam Schlöter , Martin Skutella , Khai Van Tran

The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…

General Topology · Mathematics 2025-07-03 Yuping Lv , Qi Zhao , Xuebin Chang , Wei Zeng

In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein…

Machine Learning · Computer Science 2026-02-26 Hailiang Liu , Yan-Han Chen

In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as…

Numerical Analysis · Mathematics 2013-08-06 Jean-David Benamou , Brittany D. Froese , Adam M. Oberman

The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…

Optimization and Control · Mathematics 2022-06-07 Damián Marelli , Yong Xu , Minyue Fu , Zenghong Huang

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…

Machine Learning · Computer Science 2024-04-24 Yikun Bai , Ivan Medri , Rocio Diaz Martin , Rana Muhammad Shahroz Khan , Soheil Kolouri

We propose a distributed, cubic-regularized Newton method for large-scale convex optimization over networks. The proposed method requires only local computations and communications and is suitable for federated learning applications over…

Optimization and Control · Mathematics 2020-07-08 César A. Uribe , Ali Jadbabaie

We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…

Machine Learning · Computer Science 2023-11-23 Shoichiro Takeda , Yasunori Akagi , Naoki Marumo , Kenta Niwa

Recent advances in label assignment in object detection mainly seek to independently define positive/negative training samples for each ground-truth (gt) object. In this paper, we innovatively revisit the label assignment from a global…

Computer Vision and Pattern Recognition · Computer Science 2021-03-29 Zheng Ge , Songtao Liu , Zeming Li , Osamu Yoshie , Jian Sun

We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…

In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to…

Statistics Theory · Mathematics 2022-03-18 Adrien Vacher , François-Xavier Vialard

We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…

Numerical Analysis · Mathematics 2024-11-14 Moaad Khamlich , Federico Pichi , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…

Optimization and Control · Mathematics 2023-07-12 Stefano Cipolla , Jacek Gondzio , Filippo Zanetti

We show that, on a $2$-dimensional compact manifold, the optimal transport map in the semi-discrete random matching problem is well-approximated in the $L^2$-norm by identity plus the gradient of the solution to the Poisson problem $-\Delta…

Probability · Mathematics 2019-03-29 Luigi Ambrosio , Federico Glaudo , Dario Trevisan