Related papers: A macroscopic crowd motion model of gradient flow …
We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We…
In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…
In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd - usually a fixed…
This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is…
We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density…
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
A recent study [D. Helbing, A. Johansson and H. Z. Al-Abideen, {\it Phys. Rev. E} 75, 046109 (2007)] has revealed a "turbulent" state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling…
A series of accidents caused by crowd within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on discrete element method, a granular dynamic model, in which human body is simplified…
Consider a probability measure on a Hilbert space defined via its density with respect to a Gaussian. The purpose of this paper is to demonstrate that an appropriately defined Markov chain, which is reversible with respect to the measure in…
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…
In this paper we devise a microscopic (agent-based) mathematical model for reproducing crowd behaviour in a specific scenario: a number of pedestrians, consisting of numerous social groups, flow along a corridor until a gate located at the…
The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…
We propose a macroscopic model in form of a dispersion-transport equation for non-congested flow of the athletes which is coupled to a kinematic-wave model for congested flow. The model takes into account the performance (i.e., free-flow…
A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow, is numerically solved in one space dimension using a higher-order minimizing movement scheme based on the BDF (backward differentiation formula) discretization. In…
This thesis analyze the Wasserstein gradient flow of a functional defined as a double convolution of a non-smooth repulsive interaction potential. To be more precise, the potential under investigation has a -|x| behavior close to the…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions.…
Crowd flow describes the elementary group behavior of crowds. Understanding the dynamics behind these movements can help to identify various abnormalities in crowds. However, developing a crowd model describing these flows is a challenging…