Vargas Alvarez, Hector (2026) Data-driven modelling, analysis and control of crowd dynamics. [Tesi di dottorato]

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Abstract

Complex systems exhibit emergent macroscopic behaviors arising from nonlinear interactions among large populations of agents. In application domains such as crowd dynamics, a fundamental open problem is to systematically bridge the gap between microscopic agent-based descriptions and predictive macroscopic models without relying on explicitly derived governing equations. This is essential for interpretable modeling and effective system-level numerical analysis and control tasks. The high dimensionality, heterogeneity, and nonlinearity of these systems make this micro--macro connection particularly challenging. In order to address this problem, this thesis work aims to develop a data-driven framework based on scientific machine learning and numerical analysis methods for learning macroscopic evolution operators in crowd dynamics directly from microscopic agent-based models, providing a structured foundation for system-level tasks such as state estimation and control. The central premise of this thesis is that, although microscopic agent-based dynamics evolve in very high-dimensional spaces, the associated macroscopic behavior evolves on a low-dimensional manifold embedded in a high-dimensional function space. Macroscopic observables are constructed through the systematic coarse-graining of microscopic states and subsequent numerical analysis-based manifold learning, resulting in a reduced representation that preserves essential physical properties, such as mass conservation. This reduced representation provides the foundation for identifying macroscopic evolution operators governing the emergent crowd behavior. Building on this reduced representation, the thesis formulates macroscopic crowd dynamics as the problem of identifying discrete-time evolution operators acting on the reduced macroscopic state space. In contrast to classical equation-free approaches based on local coarse time-steppers, the proposed framework identifies global macroscopic dynamics directly from data, without postulating explicit continuum equations. This operator-based formulation enables macroscopic simulations and long-horizon prediction of collective crowd behavior. Numerical results demonstrate accurate recursive prediction and stable long-horizon behavior across different crowd interaction scenarios, while maintaining computational efficiency and preserving key physical properties, such as mass conservation, by construction. The reduced evolution operators identified for crowd dynamics enable the construction of controllers and observers directly within the same macroscopic state space, thereby establishing a unified formulation that connects model identification and state estimation in an end-to-end framework. A Physics-Informed Neural Network–based scheme is employed to enforce physical consistency in the design of controllers and observers. The resulting estimation framework is first validated on benchmark dynamical systems to assess its performance and is subsequently applied to the learned crowd operators, demonstrating accurate reconstruction of macroscopic states from partial observations. In addition, a control-oriented extension is developed within the same reduced-order setting and validated on benchmark dynamical systems. The integration of the complete control architecture with the crowd-dynamics framework developed in this thesis constitutes a direction for future work.

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