Related papers: A macroscopic crowd motion model of gradient flow …
We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continuous density and the other an atomic measure. These energies…
We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modelled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional…
We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We…
Interacting particle systems provide a fundamental framework for modeling collective behavior in biological, social, and physical systems. In many applications, stochastic perturbations are essential for capturing environmental variability…
This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…
We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral Individual-Based Model of Moussaid et al, PNAS 2011, where the pedestrians are supposed to have constant speeds. This IBM supposes that…
Predicting particle segregation has remained challenging due to the lack of a general model for the segregation velocity that is applicable across a range of granular flow geometries. Here, a segregation velocity model for dense granular…
Robots operating in human-populated environments must navigate safely and efficiently while minimizing social disruption. Achieving this requires estimating crowd movement to avoid congested areas in real-time. Traditional microscopic…
We perform a convergence analysis of a discrete-in-time minimization scheme approximating a finite dimensional singularly perturbed gradient flow. We allow for different scalings between the viscosity parameter $\varepsilon$ and the time…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…
Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows. To solve them numerically, a possible approach is to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to the…
Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a…
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…
In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…
Modern methods for counting people in crowded scenes rely on deep networks to estimate people densities in individual images. As such, only very few take advantage of temporal consistency in video sequences, and those that do only impose…
We study the Wasserstein gradient flow of the Sinkhorn divergence when both the source and the target are Gaussian distributions. We prove the existence of a flow that stays in the class of Gaussian distributions, and is unique in the…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
This contribution presents experimental study of two-dimensional pedestrian flow with the aim to capture the pedestrian behaviour within the cluster formed in front of the bottleneck. Two experiments of passing through a room with one…