Mathematics

Autoencoders (AEs) are unsupervised Machine Learning (ML) algorithms which perform non-linear data compression. They are widely employed for dimensionality reduction, feature extraction and imaging processing tasks.Recently, literature showed different applications of AEs in the field of Fluid Mechanics with different algorithms developed for the prediction of flow fields. However, two of the current open problems are the interpretability of the learning procedure of a deep-learning algorithm, and the large amount of data required for training. This can be a showstopper if the data collection is computationally expensive, which is the case of high-fidelity Computational Fluid Dynamics simulations.Focus of the talk will be the recent research activities carried out within a cooperation between the University of Naples Federico II and the Stanford University on the development of AEs for accurate flow predictions past airfoils and wings.After an introduction to AEs, the talk will delve into AEs application to Aerodynamic phenomena, showing their capabilities in predicting accurate flow fields around configurations of aeronautical interest. Uncertainty quantification of AEs predictions will also be discussed, showing the importance of taking into account model-form and operative condition uncertainties when performing predictions.A discussion on a novel training algorithm (AutoEncoder with Sequential Training and Adaptive Resolution - AESTAR) to incorporate multi-fidelity data in the AEs training will conclude the talk.