Linear and nonlinear dimensionality reduction from fluid mechanics to machine learning

Abstract Dimensionality reduction is the essence of many data processing problems, including filtering, compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in fluid dynamics community, nonlinear from machine learning are becoming increasingly popular. This article, halfway between a review tutorial, introduces general framework for dimensionality techniques. Differences links autoencoders manifold methods highlighted, popular techniques such as kernel principal component analysis, isometric feature locally embedding placed this framework. These algorithms benchmarked three classic problems: (a) (b) identification oscillatory patterns, (c) compression. Their performances compared against traditional proper orthogonal decomposition to provide perspective on their diffusion dynamics.