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In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We will assume that there is no…

Optimization and Control · Mathematics 2020-04-02 Michel Duprez , Morgan Morancey , Francesco Rossi

The motion of pedestrians is subject to a wide range of influences and exhibits a rich phenomenology. To enable precise measurement of the density and velocity we use an alternative definition using Voronoi diagrams which exhibits smaller…

This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of…

Mathematical Physics · Physics 2011-03-29 Benedetto Piccoli , Andrea Tosin

In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front…

Numerical Analysis · Mathematics 2016-02-11 Mohamed Benyahia , Massimiliano Daniele Rosini

Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are…

Dynamical Systems · Mathematics 2014-02-04 Christian Marschler , Jan Sieber , Poul G. Hjorth , Jens Starke

In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during…

Data Structures and Algorithms · Computer Science 2024-07-03 Bubai Manna , Bodhayan Roy , Vorapong Suppakitpaisarn

In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is…

Numerical Analysis · Mathematics 2016-12-14 Antoine Tordeux , Guillaume Costeseque , Michael Herty , Armin Seyfried

We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…

Cellular Automata and Lattice Gases · Physics 2013-07-02 Pierre Degond , Michael Herty , Jian-Guo Liu

We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…

Machine Learning · Statistics 2025-05-29 Gabriele Visentin , Patrick Cheridito

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…

Optimization and Control · Mathematics 2019-11-11 Simone Cacace , Fabio Camilli , Raul De Maio , Andrea Tosin

A novel methodology is developed for the solution of the data-driven Monge optimal transport barycenter problem, where the pushforward condition is formulated in terms of the statistical independence between two sets of random variables:…

Optimization and Control · Mathematics 2025-12-17 Andrew D. Lipnick , Esteban G. Tabak , Giulio Trigila , Yating Wang , Xuancheng Ye , Wenjun Zhao

Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…

Analysis of PDEs · Mathematics 2017-01-10 Guillaume Carlier , Vincent Duval , Gabriel Peyré , Bernhard Schmitzer

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…

Analysis of PDEs · Mathematics 2015-09-08 David Kinderlehrer , Léonard Monsaingeon , Xiang Xu

In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…

Numerical Analysis · Mathematics 2020-11-02 Chen Liu , Deep Ray , Christopher Thiele , Lu Lin , Beatrice Riviere

We focus on robot navigation in crowded environments. The challenge of predicting the motion of a crowd around a robot makes it hard to ensure human safety and comfort. Recent approaches often employ end-to-end techniques for robot control…

We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…

Machine Learning · Statistics 2022-09-30 Qiang Liu

As a profound example of spontaneous motion, we analyze the motion of a camphor particle on a water surface. The motion is modeled as an initial-boundary value problem for a coupled nonlinear system of a diffusion equation and an ordinary…

Analysis of PDEs · Mathematics 2020-01-09 Jishan Fan , Masaharu Nagayama , Gen Nakamura , Masaaki Uesaka

Pedestrian modeling is a good way to predict pedestrian movement and thus can be used for controlling pedestrian crowds and guiding evacuations in emergencies. In this paper, we propose a pedestrian movement model based on artificial neural…

Physics and Society · Physics 2019-12-18 Xuedan Zhao , Long Xia , Jun Zhang , Weiguo Song

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual…

Numerical Analysis · Mathematics 2009-01-09 Bertrand Maury , Juliette Venel

Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…

Numerical Analysis · Mathematics 2020-03-04 Yerlan Amanbek , Mary Wheeler