Related papers: Prediction-Correction Pedestrian Flow by Means of …
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…
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…
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…
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…
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…
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…
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…
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…
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…
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:…
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…
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…
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…
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…
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…
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…
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…
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…