Compressing fluid flows with nonlinear machine learning: mode decomposition, latent modeling, and flow control

An autoencoder is a self-supervised machine-learning network trained to output a quantity identical to the input. Owing to its structure possessing a bottleneck with a lower dimension, an autoencoder works to achieve data compression, extracting the essence of the high-dimensional data into the resulting latent space. We review the fundamentals of flow field compression using convolutional neural network-based autoencoder (CNN-AE) and its applications to various fluid dynamics problems. We cover the structure and the working principle of CNN-AE with an example of unsteady flows while examining the theoretical similarities between linear and nonlinear compression techniques. Representative applications of CNN-AE to various flow problems, such as mode decomposition, latent modeling, and flow control, are discussed. Throughout the present review, we show how the outcomes from the nonlinear machine-learning-based compression may support modeling and understanding a range of fluid mechanics problems.