Extreme statistics and extreme events in dynamical models of turbulence.

We present a study of the intermittent properties of a shell model of turbulence with statistics of ∼10^{7} eddy turn over time, achieved thanks to an implementation on a large-scale parallel GPU factory. This allows us to quantify the inertial range anomalous scaling properties of the velocity fluctuations up to the 24th-order moment. Through a careful assessment of the statistical and systematic uncertainties, we show that none of the phenomenological and theoretical models previously proposed in the literature to predict the anomalous power-law exponents in the inertial range are in agreement with our high-precision numerical measurements. We find that at asymptotically high-order moments, the anomalous exponents tend toward a linear scaling, suggesting that extreme turbulent events are dominated by one leading singularity. We found that systematic corrections to scaling induced by the infrared and ultraviolet (viscous) cutoffs are the main limitations to precision for low-order moments, while high orders are mainly affected by the finite statistical samples.. The high-fidelity numerical results reported in this work offer an ideal benchmark for the development of future theoretical models of intermittency in dynamical systems for either extreme events (high-order moments) or typical fluctuations (low-order moments). For the latter, we show that we achieve a precision in the determination of the inertial range scaling exponents of the order of one part over ten thousand (fifth significant digit), which may be considered a record for out-of-equilibrium fluid-mechanics systems and models.

Stochastic fluctuations of diluted pedestrian dynamics along curved paths.

As we walk towards our destinations, our trajectories are constantly influenced by the presence of obstacles and infrastructural elements; even in the absence of crowding our paths are often curved. Since the early 2000s pedestrian dynamics have been extensively studied, aiming at quantitative models with both fundamental and technological relevance. Walking kinematics along straight paths have been experimentally investigated and quantitatively modeled in the diluted limit (i.e., in absence of pedestrian-pedestrian interactions). It is natural to expect that models for straight paths may be an accurate approximations of the dynamics even for paths with curvature radii much larger than the size of a single person. Conversely, as paths curvature increase one may expect larger and larger deviations. As no clear experimental consensus has been reached yet in the literature, here we accurately and systematically investigate the effect of paths curvature on diluted pedestrian dynamics. Thanks to a extensive and highly accurate set of real-life measurements campaign, we derive a Langevin-like social-force model quantitatively compatible with both averages and fluctuations of the walking dynamics. Leveraging on the differential geometric notion of covariant derivative, we generalize previous work by some of the authors, effectively casting a Langevin social-force model for the straight walking dynamics in a curved geometric setting. We deem this the necessary first step to understand and model the more general and ubiquitous case of pedestrians following curved paths in the presence of crowd traffic.

How neural networks learn to classify chaotic time series.

We tackle the outstanding issue of analyzing the inner workings of neural networks trained to classify regular-vs-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 (LKCNNs), recently introduced by Boullé et al. [403, 132261 (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. We show that LKCNN models trained from random weight initialization, end in two most common performance groups: one with relatively low performance (0.72 average classification accuracy) and one with high classification performance (0.94 average classification accuracy). Notably, the models in the low performance class display periodic activations that are qualitatively similar to those exhibited by LKCNNs with random weights. This could give very general criteria for identifying, a priori, trained weights that yield poor accuracy.

Toward learning Lattice Boltzmann collision operators.

In this work, we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate the performance of the resulting LBM method in reproducing time dynamics of several canonical flows. In the current study, as a first attempt to address the learning problem, the data were generated by a single relaxation time BGK operator. We demonstrate that vanilla NN architecture has very limited accuracy. On the other hand, by embedding physical properties, such as conservation laws and symmetries, it is possible to dramatically increase the accuracy by several orders of magnitude and correctly reproduce the short and long time dynamics of standard fluid flows.

Steering self-organisation through confinement.

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Fluctuations in pedestrian dynamics routing choices.

Routing choices of walking pedestrians in geometrically complex environments are regulated by the interplay of a multitude of factors such as local crowding, (estimated) time to destination, and (perceived) comfort. As individual choices combine, macroscopic traffic flow patterns emerge. Understanding the physical mechanisms yielding macroscopic traffic distributions in environments with complex geometries is an outstanding scientific challenge, with implications in the design and management of crowded pedestrian facilities. In this work, we analyze, by means of extensive real-life pedestrian tracking data, unidirectional flow dynamics in an asymmetric setting, as a prototype for many common complex geometries. Our environment is composed of a main walkway and a slightly longer detour. Our measurements have been collected during a dedicated high-accuracy pedestrian tracking campaign held in Eindhoven (The Netherlands). We show that the dynamics can be quantitatively modeled by introducing a collective discomfort function, and that fluctuations on the behavior of single individuals are crucial to correctly recover the global statistical behavior. Notably, the observed traffic split substantially departs from an optimal, transport-wise, partition, as the global pedestrian throughput is not maximized.

Deep learning velocity signals allow quantifying turbulence intensity.

Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong and statistically nontrivial fluctuations of the velocity field, and it can be quantitatively described only in terms of statistical averages. Strong nonstationarities impede statistical convergence, precluding quantifying turbulence, for example, in terms of turbulence intensity or Reynolds number. Here, we show that by using deep neural networks, we can accurately estimate the Reynolds number within 15% accuracy, from a statistical sample as small as two large-scale eddy turnover times. In contrast, physics-based statistical estimators are limited by the convergence rate of the central limit theorem and provide, for the same statistical sample, at least a hundredfold larger error. Our findings open up previously unexplored perspectives and the possibility to quantitatively define and, therefore, study highly nonstationary turbulent flows as ordinarily found in nature and in industrial processes.

Monitoring physical distancing for crowd management: Real-time trajectory and group analysis.

Physical distancing, as a measure to contain the spreading of Covid-19, is defining a "new normal". Unless belonging to a family, pedestrians in shared spaces are asked to observe a minimal (country-dependent) pairwise distance. Coherently, managers of public spaces may be tasked with the enforcement or monitoring of this constraint. As privacy-respectful real-time tracking of pedestrian dynamics in public spaces is a growing reality, it is natural to leverage on these tools to analyze the adherence to physical distancing and compare the effectiveness of crowd management measurements. Typical questions are: "in which conditions non-family members infringed social distancing?", "Are there repeated offenders?", and "How are new crowd management measures performing?". Notably, dealing with large crowds, e.g. in train stations, gets rapidly computationally challenging. In this work we have a two-fold aim: first, we propose an efficient and scalable analysis framework to process, offline or in real-time, pedestrian tracking data via a sparse graph. The framework tackles efficiently all the questions mentioned above, representing pedestrian-pedestrian interactions via vector-weighted graph connections. On this basis, we can disentangle distance offenders and family members in a privacy-compliant way. Second, we present a thorough analysis of mutual distances and exposure-times in a Dutch train platform, comparing pre-Covid and current data via physics observables as Radial Distribution Functions. The versatility and simplicity of this approach, developed to analyze crowd management measures in public transport facilities, enable to tackle issues beyond physical distancing, for instance the privacy-respectful detection of groups and the analysis of their motion patterns.

Pedestrian orientation dynamics from high-fidelity measurements.

We investigate in real-life conditions and with very high accuracy the dynamics of body rotation, or yawing, of walking pedestrians-a highly complex task due to the wide variety in shapes, postures and walking gestures. We propose a novel measurement method based on a deep neural architecture that we train on the basis of generic physical properties of the motion of pedestrians. Specifically, we leverage on the strong statistical correlation between individual velocity and body orientation: the velocity direction is typically orthogonal with respect to the shoulder line. We make the reasonable assumption that this approximation, although instantaneously slightly imperfect, is correct on average. This enables us to use velocity data as training labels for a highly-accurate point-estimator of individual orientation, that we can train with no dedicated annotation labor. We discuss the measurement accuracy and show the error scaling, both on synthetic and real-life data: we show that our method is capable of estimating orientation with an error as low as [Formula: see text]. This tool opens up new possibilities in the studies of human crowd dynamics where orientation is key. By analyzing the dynamics of body rotation in real-life conditions, we show that the instantaneous velocity direction can be described by the combination of orientation and a random delay, where randomness is provided by an Ornstein-Uhlenbeck process centered on an average delay of [Formula: see text]. Quantifying these dynamics could have only been possible thanks to a tool as precise as that proposed.

Fluctuations around mean walking behaviors in diluted pedestrian flows.

Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.

Parameter estimation of social forces in pedestrian 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.