Related papers: Control and estimation of multi-commodity network …
The subject of this work has its roots in the so called Schroedginer Bridge Problem (SBP) which asks for the most likely distribution of Brownian particles in their passage between observed empirical marginal distributions at two distinct…
Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain…
Multimarginal optimal transport (MOT) has emerged as a useful framework for many applied problems. However, compared to the well-studied classical two-marginal optimal transport theory, analysis of MOT is far more challenging and remains…
This study employs a neural network that represents the solution to a Schr\"odinger bridge problem to perform super-resolution of 2-m temperature in an urban area. Schr\"odinger bridges generally describe transformations between two data…
We investigate the martingale Schr\"odinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that this construction extends naturally to…
The Schr\"odinger bridge problem (SBP) seeks to find the measure $\hat{\mathbf{P}}$ on a certain path space which interpolates between state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL…
We derive a monotonicity property for general, transient flows of a commodity transferred throughout a network, where the flow is characterized by density and mass flux dynamics on the edges with density continuity and mass balance…
Schr\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However,…
A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers,…
We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal…
We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure…
Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a…
Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in…
A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…
Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a…
We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…
Entropic Optimal Transport (EOT), also referred to as the Schr\"odinger problem, seeks to find a random processes with prescribed initial/final marginals and with minimal relative entropy with respect to a reference measure. The relative…
In 1966, Edward Nelson presented an interesting derivation of the Schrodinger equation using Brownian motion. Recently, this derivation is linked to the theory of optimal transport, which shows that the Schrodinger equation is a Hamiltonian…
Schr\"{o}dinger bridge is a diffusion process that steers a given distribution to another in a prescribed time while minimizing the effort to do so. It can be seen as the stochastic dynamical version of the optimal mass transport, and has…
We introduce an optimum principle for a vehicular traffic network with road bottlenecks. This network breakdown minimization (BM) principle states that the network optimum is reached, when link flow rates are assigned in the network in such…