相关论文: Gini-regularized Optimal Transport with an Applica…

We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…

We study the forecasting problem for traffic with dynamic, possibly periodical, and joint spatial-temporal dependency between regions. Given the aggregated inflow and outflow traffic of regions in a city from time slots 0 to t-1, we predict…

This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…

Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…

Clock synchronization is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronization needed over…

Optimal transport (OT), and in particular the Wasserstein distance, has seen a surge of interest and applications in machine learning. However, empirical approximation under Wasserstein distances suffers from a severe curse of…

In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…

In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a…

Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…

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…

Motion planning classically concerns the problem of accomplishing a goal configuration while avoiding obstacles. However, the need for more sophisticated motion planning methodologies, taking temporal aspects into account, has emerged. To…

Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off,…

We study the Unbalanced Optimal Transport (UOT) between two measures of possibly different masses with at most $n$ components, where the marginal constraints of standard Optimal Transport (OT) are relaxed via Kullback-Leibler divergence…

Spatio-temporal forecasting is an open research field whose interest is growing exponentially. In this work we focus on creating a complex deep neural framework for spatio-temporal traffic forecasting with comparatively very good…

Classical field forecast evaluation relies mainly on local scores such as RMSE or MAE. These metrics severely over-penalize small spatial or temporal displacements of coherent structures, a limitation known as the double-penalty issue and…

This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…

Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…

To ensure the safety of railroad operations, it is important to monitor and forecast track geometry irregularities. A higher safety requires forecasting with higher spatiotemporal frequencies, which in turn requires capturing spatial…

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…

Traffic flow forecasting is essential for managing congestion, improving safety, and optimizing various transportation systems. However, it remains a prevailing challenge due to the stochastic nature of urban traffic and environmental…