Comparing first order microscopic and macroscopic crowd models for an increasing number of massive agents

In this paper a comparison between first order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number $N$ of pedestrians. The novelty is the fact of considering massive agents, namely particles whose individual mass does not become infinitesimal when $N$ grows. This implies that the total mass of the system is not constant but grows with $N$. The main result is that the two types of models approach one another in the limit $N\to\infty$, provided the strength and/or the domain of pedestrian interactions are properly modulated by $N$ at either scale. This is consistent with the idea that pedestrians may adapt their interpersonal attitudes according to the overall level of congestion.Comment: 26 pages, 8 figure

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries, and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed and a solution strategy is proposed.Comment: 23 pages, 10 figures in J. Engrg. Math., 201

Parameter Estimation of Social Forces in Crowd Dynamics Models via a Probabilistic Method

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.Comment: 20 pages, 9 figure

Continuous measurements of real-life bidirectional pedestrian flows on a wide walkway

Employing partially overlapping overhead \kinectTMS sensors and automatic pedestrian tracking algorithms we recorded the crowd traffic in a rectilinear section of the main walkway of Eindhoven train station on a 24/7 basis. Beside giving access to the train platforms (it passes underneath the railways), the walkway plays an important connection role in the city. Several crowding scenarios occur during the day, including high- and low-density dynamics in uni- and bi-directional regimes. In this paper we discuss our recording technique and we illustrate preliminary data analyses. Via fundamental diagrams-like representations we report pedestrian velocities and fluxes vs. pedestrian density. Considering the density range $0$ - $1.1\,$ped/m$^2$, we find that at densities lower than $0.8\,$ped/m$^2$ pedestrians in unidirectional flows walk faster than in bidirectional regimes. On the opposite, velocities and fluxes for even bidirectional flows are higher above $0.8\,$ped/m$^2$.Comment: 9 pages, 7 figure

Modeling Routing Choices in Unidirectional Pedestrian Flows

In this work we present a simple routing model capable of capturing pedestrians path choices in the presence of a herding effect. The model is tested and validated against data from a large scale tracking campaign which we have conducted during the GLOW 2019 festival. The choice between alternative paths is modeled as an individual cost minimization procedure, with the cost function being associated to the (estimated) traveling time. In order to trigger herding effects the cost function is supplemented with a penalty term, modulated as a function of the fraction of pedestrians walking along each route. The model is shown to provide an accurate quantitative description of the decision process

RSSi-Based Visitor Tracking in Museums via Cascaded AI Classifiers and Coloured Graph Representations

Individual tracking of museum visitors based on portable radio beacons, an asset for behavioural analyses and comfort/performance improvements, is seeing increasing diffusion. Conceptually, this approach enables room-level localisation based on a network of small antennas (thus, without invasive modification of the existent structures). The antennas measure the intensity (RSSi) of self-advertising signals broadcasted by beacons individually assigned to the visitors. The signal intensity provides a proxy for the distance to the antennas and thus indicative positioning. However, RSSi signals are well-known to be noisy, even in ideal conditions (high antenna density, absence of obstacles, absence of crowd, ...). In this contribution, we present a method to perform accurate RSSi-based visitor tracking when the density of antennas is relatively low, e.g. due to technical constraints imposed by historic buildings. We combine an ensemble of "simple" localisers, trained based on ground-truth, with an encoding of the museum topology in terms of a total-coloured graph. This turns the localisation problem into a cascade process, from large to small scales, in space and in time. Our use case is visitors tracking in Galleria Borghese, Rome (Italy), for which our method manages >96% localisation accuracy, significantly improving on our previous work (J. Comput. Sci. 101357, 2021)

Path-integral representation of diluted pedestrian dynamics

We frame the issue of pedestrian dynamics modeling in terms of path-integrals, a formalism originally introduced in quantum mechanics to account for the behavior of quantum particles, later extended to quantum field theories and to statistical physics. Path-integration enables a trajectory-centric representation of the pedestrian motion, directly providing the probability of observing a given trajectory. This appears as the most natural language to describe the statistical properties of pedestrian dynamics in generic settings. In a given venue, individual trajectories can belong to many possible usage patterns and, within each of them, they can display wide variability. We provide first a primer on path-integration, and we introduce and discuss the path-integral functional probability measure for pedestrian dynamics in the diluted limit. As an illustrative example, we connect the path-integral description to a Langevin model that we developed previously for a particular crowd flow condition (the flow in a narrow corridor). Building on our previous real-life measurements, we provide a quantitatively correct path-integral representation for this condition. Finally, we show how the path-integral formalism can be used to evaluate the probability of rare-events (in the case of the corridor, U-turns)

How neural networks learn to classify chaotic time series

Neural networks are increasingly employed to model, analyze and control non-linear dynamical systems ranging from physics to biology. Owing to their universal approximation capabilities, they regularly outperform state-of-the-art model-driven methods in terms of accuracy, computational speed, and/or control capabilities. On the other hand, neural networks are very often they are taken as black boxes whose explainability is challenged, among others, by huge amounts of trainable parameters. In this paper, we tackle the outstanding issue of analyzing the inner workings of neural networks trained to classify regular-versus-chaotic time series. This setting, well-studied in dynamical systems, enables thorough formal analyses. We focus specifically on a family of networks dubbed Large Kernel Convolutional Neural Networks (LKCNN), recently introduced by Boull\'{e} et al. (2021). These non-recursive networks have been shown to outperform other established architectures (e.g. residual networks, shallow neural networks and fully convolutional networks) at this classification task. Furthermore, they outperform ``manual'' classification approaches based on direct reconstruction of the Lyapunov exponent. We find that LKCNNs use qualitative properties of the input sequence. In particular, we show that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models. Low performing models show, in fact, analogous periodic activations to random untrained models. This could give very general criteria for identifying, a priori, trained models that have poor accuracy