The robustness of an artificial neural network that performs model order reduction for flow field data is studied. The network is trained with a large-scale distributed learning approach using up to 6,259 nodes of the supercomputer Fugaku. Flow around two square cylinders with a varying distance between their centers is investigated. The network is trained and tested with data from numerical simulations. First, the capability to reproduce flow fields with 2, 12, and 24 modes is investigated by comparing the reconstructed flow data to simulated data. It is shown, that reconstructions based on 2 modes cannot capture both, low- and high-frequency flow structures correctly, whereas predictions based on 12 and 24 modes yield improved flow fields, especially in the case of high-frequency waves in the vicinity of the square cylinders. Reconstructions with 24 modes provide smooth velocity fields that reproduce all relevant low- and high-frequency waves for all variations of the distance between the two square cylinders. Second, the performance of the machine learning-based reconstructions are compared to proper orthogonal decomposition, which is a commonly used reduced order model technique. The comparison only includes flow fields based on 24 modes. For all geometric variations, the mean squared errors of the reconstructions by the conventional method are higher than those of the machine learning model. This underlines the advantage of artificial neural networks over linear methods like proper orthogonal decomposition for tasks like reconstructing flow fields that are characterized by non-linear governing equations.

The application of Artificial Neural Networks (ANNs) has been extensively investigated for fluid dynamic problems. A specific form of ANNs are Physics-Informed Neural Networks (PINNs). They incorporate physical laws in the training and have increasingly been explored in the last few years. In this work, the prediction accuracy of PINNs is compared with that of conventional Deep Neural Networks (DNNs). The accuracy of a DNN depends on the amount of data provided for training. The change in prediction accuracy of PINNs and DNNs is assessed using a varying amount of training data. To ensure the correctness of the training data, they are obtained from analytical and numerical solutions of classical problems in fluid mechanics. The objective of this work is to quantify the fraction of training data relative to the maximum number of data points available in the computational domain, such that the accuracy gained with PINNs justifies the increased computational cost. Furthermore, the effects of the location of sampling points in the computational domain and noise in training data are analyzed. In the considered problems, it is found that PINNs outperform DNNs when the sampling points are positioned in the Regions of Interest. PINNs for predicting potential flow around a Rankine oval have shown a better robustness against noise in training data compared to DNNs. Both models show higher prediction accuracy when sampling points are randomly positioned in the flow domain as compared to a prescribed distribution of sampling points. The findings reveal new insights on the strategies to massively improve the prediction capabilities of PINNs with respect to DNNs.

As evidenced by the worldwide pandemic, respiratory infectious diseases and their airborne transmission must be studied to safeguard public health. This study focuses on the emission and transport of speech-generated droplets, which can pose risk of infection depending on the loudness of the speech, its duration and the initial angle of exhalation. We have numerically investigated the transport of these droplets into the human respiratory tract by way of a natural breathing cycle in order to predict the infection probability of three strains of SARS-CoV-2 on a person who is listening at a one-meter distance. Numerical methods were used to set the boundary conditions of the speaking and breathing models and large eddy simulation (LES) was used for the unsteady simulation of approximately 10 breathing cycles. Four different mouth angles when speaking were contrasted to evaluate real conditions of human communication and the possibility of infection. Breathed virions were counted using two different approaches: the breathing zone of influence and direction deposition on the tissue. Our results show that infection probability drastically changes based on the mouth angle and the breathing zone of influence overpredicts the inhalation risk in all cases. We conclude that to portray real conditions, the probability of infection should be based on direct tissue deposition results to avoid overprediction and that several mouth angles must be considered in future analyses.