Data-driven crowd dynamics using kinetic theory and ensemble-based data assimilation

Understanding pedestrian dynamics is critical for mitigating crowd-related risks and improving public safety. In this work, we propose a novel data-driven mesoscopic modeling framework that combines the kinetic theory of active particles (KTAPs) with data assimilation techniques, thereby offering a data-driven learning approach applicable to collective systems with learning and decision-making behavior, in line with recent KTAP developments in this area. The framework uses an ensemble Kalman filter to sequentially estimate the time-dependent spatial distribution of pedestrians and model parameters by fusing observations with the mesoscopic forward model state. Through a series of twin experiments, we show that the panic factor-a key behavioral parameter-is identifiable within this framework. We also evaluate the robustness of the approach by assimilating synthetic observations generated by an agent-based model (ABM). This setup introduces structural model error because the ABM is governed by microscopic rules that differ fundamentally from the mesoscopic kinetic equations. Despite this discrepancy, the ensemble Kalman filter, through the observation-based innovation term, successfully drives the kinetic model to track the observed pedestrian density while simultaneously recovering the panic factor. In this framework, observations act as a physical constraint on the evolution of the kinetic model. Crowd-dynamics models, including ABMs and kinetic models, often rely on phenomenological terms to describe social interactions, with parameters that are highly uncertain. Our findings indicate that in such systems, free-running simulations inevitably may diverge from the true state, whereas an online data-driven approach effectively constrains the system's trajectory to its underlying dynamical manifold.