There has been growing interest in crowd dynamics modelling, driven especially by its relevance in various fields including urban planning, safety measure and event management. The central objective within this field is to understand how group of people behave collectively due to the interactions, movements and responses to environmental factors. The recent progress in machine learning has significantly impacted crowd dynamics modelling, utilizing vast amount of data from sensors, digital devices and simulations. Data-driven methods have demonstrated the ability to achieve more flexible and precise predictions of dynamics, even without knowing the governing equation of the systems.

This study focuses on crowd dynamics modelling with a data-driven method, the Koopman operator, which is an infinite dimensional linear operator that acts on functions defined on the state space of a dynamical system. The primary objective is to parameterize the Koopman operator to accommodate variable geometries and conditions in crowd dynamics prediction. The Koopman operator offers insights into system dynamics through eigencomponents via extended dynamic mode decomposition, a novel method to approximate the infinite dimensional Koopman operator with linear combination of eigenfunctions, eigenvalues and modes in infinite dimension.

The data on crowd dynamics is gathered using Vadere, an open-source crowd simulation software. Through the Koopman operator, the essential components of the dynamic system are identified, represented by eigenfunctions. It enabled successful predictions of unknown crowd behaviour. Further investigation of the eigencomponents of the Koopman operator is conducted to characterize coherent structures in the dynamic systems. The Koopman eigenfunctions reveal wave-like data intrinsic patterns and the parameter-dependent trends in crowd behaviours.