Linear and Nonlinear Dimensionality Reduction from Fluid Mechanics to Machine Learning

Abstract

Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community, nonlinear tools from machine learning are becoming increasingly popular. This article, halfway between a review and a tutorial, introduces a general framework for linear and nonlinear dimensionality reduction techniques. Differences and links between autoencoders and manifold learning methods are highlighted, and popular nonlinear techniques such as kernel Principal Component Analysis (kPCA), isometric feature learning (ISOMAPs) and Locally Linear Embedding (LLE) are placed in this framework. These algorithms are benchmarked in three classic problems: 1) filtering, 2) identification of oscillatory patterns, and 3) data compression. Their performances are compared against the traditional Proper Orthogonal Decomposition (POD) to provide a perspective on their diffusion in fluid dynamics.

A two-stage deep learning framework for early-stage lifetime prediction for lithium-ion batteries with consideration of features from multiple cycles

“…Moreover, statistical and machine learning approaches are attractive, with the recent improvement in algorithms and computational power, and the growing availability of battery cycling data. Nowadays, many studies have been done using these advanced methods to address engineering problems, such as computational fluid dynamics, molecular design, and so on (Reich, 1997;Liakos et al, 2018;Sanchez-Lengeling and Aspuru-Guzik, 2018;Brunton et al, 2020;Hegde and Rokseth, 2020;Mendez, 2022). Nonetheless, these techniques are also applied in predicting battery lifetime.…”