Séminaire du LPTMS : Denis Ullmo (LPTMS)

A Mean Field Game description of pedestrian dynamic

Denis Ullmo (Laboratoire de Physique Théorique et Modèles Statistiques)

Onsite seminar + zoom (ID: 962 4404 9550, PW: 9thN9E).

In this talk, I will consider the dynamics of crowds at the « operational » level, which corresponds to the relatively short time and length scale associated for instance with a single obstacle. Comparing various model predictions with experimental data, I will show that, contrarily to what is usually assumed in such context, it is necessary to take into account the fact that pedestrian have the capacity to « anticipate » to reproduce even the qualitative properties of the experimental data. Models based on a analogy with granular materials therefore fails drastically, and even modern models of crowds dynamics including short term (ie up to the next collision) anticipation are unable to reproduce the essential feature of the experiments.

Furthermore, I will show that a very simple model based on Mean Field Game, that can be analyzed through a very elegant connection with the non-linear Schrödinger equation, is able (actually by construction) to take into account the effects of anticipation of the pedestrians, and reproduce nicely the important features of the experiment.

Date/Time : 07/12/2021 - 11:00 - 12:00

Location : Petit amphi, bâtiment Pascal n° 530