### 2020

Joris Willems; Alessandro Corbetta; Vlado Menkovski; Federico Toschi

Pedestrian orientation dynamics from high-fidelity measurements Journal Article

In: arXiv, 2020.

Abstract | BibTeX | Tags: cs.LG, physics.soc-ph

@article{0c6a159182504960bcab1be66495fb3c,

title = {Pedestrian orientation dynamics from high-fidelity measurements},

author = {Joris Willems and Alessandro Corbetta and Vlado Menkovski and Federico Toschi},

year = {2020},

date = {2020-01-01},

journal = {arXiv},

publisher = {Cornell University Library},

abstract = {We investigate in real-life conditions and with very high accuracy the dynamics of body rotation, or yawing, of walking pedestrians - an 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 7.5 degrees. 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 100ms. Quantifying these dynamics could have only been possible thanks to a tool as precise as that proposed.},

keywords = {cs.LG, physics.soc-ph},

pubstate = {published},

tppubtype = {article}

}

We investigate in real-life conditions and with very high accuracy the dynamics of body rotation, or yawing, of walking pedestrians - an 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 7.5 degrees. 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 100ms. Quantifying these dynamics could have only been possible thanks to a tool as precise as that proposed.

### 2019

Alessandro Corbetta; Vlado Menkovski; Roberto Benzi; Federico Toschi

Deep learning velocity signals allows to quantify turbulence intensity Journal Article

In: arXiv, 2019.

Abstract | BibTeX | Tags: cond-mat.stat-mech, cs.AI, cs.LG, physics.flu-dyn

@article{046d24a1bab542e983a477781595c64f,

title = {Deep learning velocity signals allows to quantify turbulence intensity},

author = {Alessandro Corbetta and Vlado Menkovski and Roberto Benzi and Federico Toschi},

year = {2019},

date = {2019-01-01},

journal = {arXiv},

publisher = {Cornell University Library},

abstract = {Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong and statistically non-trivial fluctuations of the velocity field, over a wide range of length- and time-scales, and it can be quantitatively described only in terms of statistical averages. Strong non-stationarities hinder the possibility to achieve statistical convergence, making it impossible to define the turbulence intensity and, in particular, its basic dimensionless estimator, the Reynolds number. Here we show that by employing Deep Neural Networks (DNN) 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 rate of convergence of the central limit theorem, and provide, for the same statistical sample, an error at least $100$ times larger. Our findings open up new perspectives in the possibility to quantitatively define and, therefore, study highly non-stationary turbulent flows as ordinarily found in nature as well as in industrial processes.},

keywords = {cond-mat.stat-mech, cs.AI, cs.LG, physics.flu-dyn},

pubstate = {published},

tppubtype = {article}

}

Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong and statistically non-trivial fluctuations of the velocity field, over a wide range of length- and time-scales, and it can be quantitatively described only in terms of statistical averages. Strong non-stationarities hinder the possibility to achieve statistical convergence, making it impossible to define the turbulence intensity and, in particular, its basic dimensionless estimator, the Reynolds number. Here we show that by employing Deep Neural Networks (DNN) 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 rate of convergence of the central limit theorem, and provide, for the same statistical sample, an error at least $100$ times larger. Our findings open up new perspectives in the possibility to quantitatively define and, therefore, study highly non-stationary turbulent flows as ordinarily found in nature as well as in industrial processes.