Related papers: Prediction-Correction Pedestrian Flow by Means of …
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a micro-robot or active particle -- that is advected by a two-dimensional flow,…
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…
This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…
This paper presents a novel context-based approach for pedestrian motion prediction in crowded, urban intersections, with the additional flexibility of prediction in similar, but new, environments. Previously, Chen et. al. combined…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
One of the most popular approaches to multi-target tracking is tracking-by-detection. Current min-cost flow algorithms which solve the data association problem optimally have three main drawbacks: they are computationally expensive, they…
An average pedestrian flow through an exit is one of the most important index in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model by using cellular automaton, is extended by…
Fluid approximation is a widely used approach for solving two-stage stochastic optimization problems, with broad applications in service system design such as call centers and healthcare operations. However, replacing the underlying random…
Due to computational complexity, fluid flow problems are mostly defined on a bounded domain. Hence, capturing fluid outflow calls for imposing an appropriate condition on the boundary where the said outflow is prescribed. Usually, the…
This paper concerns optimal control of a nonconvex perturbed sweeping process and its applications to optimization of the planar crowd motion model of traffic equilibria. The obtained theoretical results allow us to investigate a dynamic…
To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the…
Through multiscale analysis of the adjoint Fokker-Planck equation, strict bounds are derived for the center of mass diffusivity of an overdamped harmonic chain in a periodic potential, often known as the discrete Frenkel-Kontorova model.…
This paper presents a mesoscopic traffic flow model that explicitly describes the spatio-temporal evolution of the probability distributions of vehicle trajectories. The dynamics are represented by a sequence of factor graphs, which enable…
We consider cost minimizing stopping time solutions to Skorokhod embedding problems, which deal with transporting a source probability measure to a given target measure through a stopped Brownian process. PDEs and a free boundary problem…
Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are…
We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…
We present a machine learning based approach to address the study of transport processes, ubiquitous in continuous mechanics, with particular attention to those phenomena ruled by complex micro-physics, impractical to theoretical…
We analyze numerically some macroscopic models of pedestrian motion such as Hughes model [1] and mean field game with nonlinear mobilities [2] modeling fast exit scenarios in pedestrian crowds. A model introduced by Hughes consisting of a…
We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…