Identifying elementary scenarios of pedestrian dynamics through interpretable artificial intelligence (Idefiks)

• Applicant: Professorin Dr. Gerta Köster
• Subject Area: Traffic and Transport Systems, Intelligent and Automated Traffic ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 524081074

Moving crowds form dynamic systems in which flows of people change in time and place. One phenomenon one frequently observes in this process is the emergence and dissolution of traffic jams. Experiments and simulations are conducted to understand, predict, and avoid this and other phenomena. Here, scenarios are typically described in terms of qualitative observations (there is a congestion) or in terms of static properties such as geometry and other boundary conditions (passage of width 1 meter with mean influx of 1.5 people per second). To date, there are no quantitative methods for characterizing dynamics in pedestrian research. The Idefiks project aims to close this gap: Using parameters from engineering mathematics, we will characterize the dynamics of pedestrian flows quantitatively to enable objective descriptions, analyses and comparisons of dynamics. In order to investigate the stability and periodicity of a nonlinear dynamic system of the form dX/dt= F(X(t)), the eigenvalues of the Jacobian matrix DF are used in engineering mathematics. They describe changes near stationary solutions. This could be used, for example, to detect the growth of queues or the periodic waxing and waning of densities in a crowd. However, this requires knowing F, which is rarely the case in pedestrian dynamics. Instead, only the data from measurements or simulations are available. The methodological idea of Idefiks is to use operator-based AI to learn from the data surrogate models for which mathematical analysis is possible. Specifically, I want to investigate whether the system can be characterized using the eigenvalues of the Koopman operator associated with the surrogate model. The Koopman operator K_Δt allows to compute from a current system state X(t) a future state X(t+Δt) = K_Δt ◦X(t). This relation holds even independently of the proximity to stationary solutions. Moreover, if K is learned, one no longer needs an approximation to F. We will characterize and identify elementary scenarios of pedestrian dynamics through their dynamics, thus, flanking the present descriptions. In particular, we will learn pedestrian flows and densities. We will create the software tools needed to do this and make them freely and openly available to the community. We hope the findings will improve safety analyses - whether in public transportation, buildings, or at large events. We hope to see further progress in the study and comparison of simulation models, and ultimately in the comparison of simulated data with empirical data.

• DFG Programme: Research Grants