Related papers: A macroscopic crowd motion model of gradient flow …
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…
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…
This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
Macroscopic models of crowd flow incorporating individual pedestrian choices present many analytic and computational challenges. Anisotropic interactions are particularly subtle, both in terms of describing the correct "optimal" direction…
Small-scale turbulence can be comprehensively described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling. Typical models consist of stochastic equations based on closures for…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…
In this paper we deal with the analysis of the solutions of traffic flow models at multiple scales, both in the case of a single road and of road networks. We are especially interested in measuring the distance between traffic states (as…
We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…
We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only…
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…
We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…
We present a macroscopic traffic flow model that extends existing fluid-like models by an additional term containing the second derivative of the safe velocity. Two qualitatively different shapes of the safe velocity are explored: a…
A micro-hydrodynamics model based on elastic collisions of light point solvent particles with a heavy solute particle is investigated in the setting where the light particles have velocity distribution corresponding to a background flow.…
We consider a one-dimensional kinetic model of granular media in the case where the interaction potential is quadratic. Taking advan- tage of a simple first integral, we can use a reformulation (equivalent to the initial kinetic model for…
The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages for studying related problems. In general, microscopic models…
In this paper, we aim to monitor the flow of people in large public infrastructures. We propose an unsupervised methodology to cluster people flow patterns into the most typical and meaningful configurations. By processing 3D images from a…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…