Juan Martin Guerrieri

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.

Data assimilation involves sequential inference in geophysical systems with nonlinear dynamics and observational operators. Non-parametric filters are a promising approach for data assimilation because they are able to represent non-Gaussian densities. The mapping particle filter is an iterative ensemble method that incorporates the Stein Variational Gradient Descent (SVGD) to produce a particle flow transforming state vectors from prior to posterior densities. At every pseudo-time step, the Kullback-Leibler divergence between the intermediate density and the target posterior is evaluated and minimized. However, for applications in geophysical systems, challenges persist in high dimensions, where sample covariance underestimation leads to filter divergence. This work proposes two localization methods, one in which a local kernel function is defined and the particle flow is global. The second method, given a localization radius, physically partitions the state vector and performs local mappings at each grid point. The performance of the proposed Local Mapping Particle Filters (LMPFs) is assessed in synthetic experiments. Observations are produced with a two-scale Lorenz system, while a one-scale Lorenz model is used as surrogate, introducing model error in the inference. The methods are evaluated with both full and partial observations, as well as with different linear and non-linear observational operators. The LMPFs with Gaussian mixtures in the prior density perform similarly to Gaussian filters such as the Ensemble Transform Kalman Filter (ETKF) and the Local Ensemble Transform Kalman Filter (LETKF) in most cases, and in some scenarios, they provide competitive performance in terms of analysis accuracy.

Data assimilation involves sequential inference in geophysical systems with nonlinear dynamics and observational operators. Particle filters are a promising approach for data assimilation because they are able to represent non-Gaussian densities. The mapping particle filter incorporates the Stein variational gradient descents to produce a particle flow that transforms state vectors from prior to posterior densities, aiming to minimize the Kullback-Leibler divergence. However, for applications in geophysical systems, challenges persist in high dimensions, where sample covariance underestimation leads to filter divergence. This work proposes two localization methods, one in which a local kernel function is defined and the particle flow is global. The second method, given a localization radius, physically partitions the state vector and performs local mappings at each grid point. Gaussian and Gaussian mixtures are evaluated as a prior density. The performance of the proposed Local Mapping Particle Filters (LMPFs) is assessed in synthetic experiments. Observations are produced with a two-scale Lorenz-96 system, while a single-scale Lorenz-96 is used as a surrogate model, introducing model error in the inference. The methods are evaluated with full and partial observations and with different linear and non-linear observational operators. The LMPFs with Gaussian mixtures perform similarly to Gaussian filters such as ETKF and LETKF in most cases, and in some scenarios, they provide competitive performance in terms of analysis accuracy.