Exploration and prediction of fluid dynamical systems using auto-encoder technology

Machine-learning (ML) algorithms offer a new path for investigating high-dimensional, nonlinear problems, such as flow-dynamical systems. The development of ML methods, associated with the abundance of data and combined with fluid-dynamics knowledge, offers a unique opportunity for achieving significant breakthroughs in terms of advances in flow prediction and its control. The objective of this paper is to discuss some possibilities offered by ML algorithms for exploring and predicting flow-dynamical systems. First, an overview of basic concepts underpinning artificial neural networks, deep neural networks, and convolutional neural networks is given. Building upon this overview, the concept of Auto-Encoders (AEs) is introduced. An AE constitutes an unsupervised learning technique in which a neural-network architecture is leveraged for determining a data structure that results from reducing the dimensionality of the native system. For the particular test case of flow behind a cylinder, it is shown that combinations of an AE with other ML algorithms can be used (i) to provide a low-dimensional dynamical model (a probabilistic flow prediction), (ii) to give a deterministic flow prediction, and (iii) to retrieve high-resolution data in the spatio-temporal domain from contaminated and/or under-sampled data.