Comparison of Dimensionality Reduction Techniques for Multi-Variable Spatiotemporal Flow Fields

Abstract

In the field of fluid mechanics, it is a potential consensus that nonlinear dimensionality reduction (DR) techniques outperform linear methods. However, this conclusion has been obtained based on simple fluid phenomena and an incomplete evaluation system of dimensionality reduction algorithms. In this study, we use an improved evaluation system of DR methods to compare and evaluate the performance of four DR methods, including two linear techniques: Principal Component Analysis (PCA) and Independent Component Analysis (ICA), and two non-linear techniques: Isometric Mapping (ISOMAP) and Locally Linear Embedding (LLE). The four methods are applied to analyze a complex hydrodynamic flow field with cavitation by considering the joint features of multiple variables. Results show that LLE can capture redundant features that do not contribute to understanding the characteristics of flow fields, while ISOMAP is more suitable for handling datasets with multiple scales than LLE. PCA and ISOMAP can successfully capture the characteristics and evolution of flow fields. In addition, 3D supplementary information can assist ICA in improving the problem of identifying unstable flow field states. Overall, PCA may be the more meaningful way of dimensionality reduction for complex physical problems.

Keywords: Nonlinear dimensionality reduction, Linear dimensionality reduction, Evaluation system of dimensionality reduction, Multivariate joint expression, Cavitation.