Mean-Field Games Applied to Pedestrian Dynamics
This thesis explores pedestrian dynamics through experimental observations and simulations, focusing on the operational layer of pedestrian movement. Experiments involving a controlled crowd and a moving cylindrical obstacle, reveal that pedestrians exhibit anticipatory behaviors that deviate from granular behavior. The thesis challenges two existing pedestrian dynamics models, of different complexity showing their limitations in capturing the observed anticipatory behaviors. These models are found to be too myopic, focusing on short-term decisions without adequately accounting for long-term anticipations. To address these shortcomings, this work proposes a model based on the theory of Mean-Field Games (MFG). MFG models, which combine optimal control and game theory, describe interactions among a large number of agents via their average density, simplifying the mathematical framework. The MFG model successfully predicts the experimental anticipation patterns by incorporating a discount factor that adjusts the weight of future events in the optimization process. Additionally, the thesis presents two corollary projects. The first has the goal to integrate MFG with agent-based microscopic models to handle scenarios requiring detailed individual interactions, such as evacuations. The second explores using Physics Informed Neural Networks to solve MFG equations.