LPTMS Intership and PhD Proposal: Mean Field Game description of Pedestrian Dynamics

Responsable: Denis ULLMO + 33 (0)1 69 15 74 76

Video: Mean field games

The situations where large crowds are gathered, and for which one would clearly benefit from a better ability to predict their dynamics, are numerous, and range from daily life optimization in train stations or sport events, to more dramatic circumstances such as the stampedes that have grieved the hadj in 1990 and 2015.

Predictive models for such crowd dynamics have followed essentially two strategies. The first one based on a kind of “cellular automate" approach, where one tries to identify local interaction rules between individuals. These approaches have shown some success for some animal groups such as bird flock, fish school or insect swarm, but have not provided a robust description of human crowd motion. The second strategy is to follow one of the favorite routes of condensed matter physicist and to develop a hydrodynamic description, or in terms of models analog to the ones developed for granular materials.

In some circumstances, these hydrodynamic, or granular material-like, models, fail drastically, even at the qualitative level, and they do so because, as the cellular-automate based model, they lack the ability to include the anticipation and optimization performed by the agents.

To include anticipation and optimization requires a Game Theoretical approach to the problem, which leads one to consider “many-body Game Theory” as many agents in interaction are involved.

The goal of the internship will be to address this problem of crowd dynamics in terms of a mean field approximation to the this many-body game theory that has been developed in the last decade under the name of Mean Field Game.

[For an introduction do Mean Field Games, see : “Quadratic Mean Field Games

Denis Ullmo, Igor Swiecicki, and Thierry Gobron, Physics Report 799, 1-35, (2019)]