Related papers: Prediction-Correction Pedestrian Flow by Means of …
This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is…
Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…
We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations…
This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
The two phase model for vehicular traffic flows recently appeared in \cite{goatin2006aw} and \cite{BenyahiaRosini01} is endowed with a point constraint on the flow to allow for the modelling of phenomena such as the effects of toll booths…
We study Variational Rectified Flow Matching, a framework that enhances classic rectified flow matching by modeling multi-modal velocity vector-fields. At inference time, classic rectified flow matching 'moves' samples from a source…
The ability to predict traffic flow over time for crowded areas during rush hours is increasingly important as it can help authorities make informed decisions for congestion mitigation or scheduling of infrastructure development in an area.…
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…
This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while…
We propose a model of optimal parallel transport between vector fields on a connection graph, which consists of a weighted graph along with a map from its edges to an orthogonal group. Inspired by the well-known equivalence of 1-Wasserstein…
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker--Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…
A field deterministic model of the vehicular dynamics in a generic urban street canyon with two neighboring canyons is considered. The assumed hydrodynamical model of vehicular movement is coupled to the gasdynamical model of the air and…
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In…
Traditional rule-based physical models are limited by their reliance on singular physical formulas and parameters, making it difficult to effectively tackle the intricate tasks associated with crowd simulation. Recent research has…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
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…