Data-driven physics-based modeling of pedestrian dynamics

Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous work demonstrated the effectiveness of Langevin-like equations in capturing the statistical properties of pedestrian dynamics in simple settings, such as almost straight trajectories. However, modeling more complex dynamics, such as when multiple routes and origin destinations are involved, remains a significant challenge. In this work, we introduce a novel and generic framework to describe the dynamics of pedestrians in any geometric setting, significantly extending previous works. Our model is based on Langevin dynamics with two timescales. The fast timescale corresponds to the stochastic fluctuations present when a pedestrian is walking. The slow timescale is associated with the dynamics that a pedestrian plans to follow, thus a smoother path without stochastic fluctuations. Employing a data-driven approach inspired by statistical field theories, we learn the complex potentials directly from the data, namely a high-statistics database of real-life pedestrian trajectories. This approach makes the model generic as the potentials can be read from any trajectory data set and the underlying Langevin structure enables physics-based insights. We validate our model through a comprehensive statistical analysis, comparing simulated trajectories with actual pedestrian measurements across five complementary settings of increasing complexity, including a real-life train platform scenario, underscoring its practical societal relevance. We show that our model, by learning the effective potential, captures fluctuation statistics in the dynamics of individual pedestrians, both in dilute (no interaction with other pedestrians) as well as in dense crowds conditions (in presence of interactions). Our results can be reproduced with our generic open-source Python implementation [Pouw et al. (2024) [Software] doi:10.5281/zenodo.13362271] and validated with the supplemented data set [Pouw et al. (2024) [Dataset] doi:10.5281/zenodo.13784588]. Beyond providing fundamental insights and predictive capabilities in pedestrian dynamics, our model could be used to investigate generic active dynamics such as vehicular traffic and collective animal behavior.