Comparison and evaluation of dimensionality reduction techniques for the numerical simulations of unsteady cavitation

Abstract

In the field of fluid mechanics, dimensionality reduction (DR) is widely used for feature extraction and information simplification of high-dimensional spatiotemporal data. It is well known that nonlinear DR techniques outperform linear methods, and this conclusion may have reached a consensus in the field of fluid mechanics. However, this conclusion is derived from an incomplete evaluation of the DR techniques. In this paper, we propose a more comprehensive evaluation system for DR methods and compare and evaluate the performance differences of three DR methods: principal component analysis (PCA), isometric mapping (isomap), and independent component analysis (ICA), when applied to cavitation flow fields. The numerical results of the cavitation flow are obtained by solving the compressible homogeneous mixture model. First, three different error metrics are used to comprehensively evaluate reconstruction errors. Isomap significantly improves the preservation of nonlinear information and retains the most information with the fewest modes. Second, Pearson correlation can be used to measure the overall structural characteristics of the data, while dynamic time warping cannot. PCA performs the best in preserving the overall data characteristics. In addition, based on the uniform sampling-based K-means clustering proposed in this paper, it becomes possible to evaluate the local structural characteristics of the data using clustering similarity. PCA still demonstrates better capability in preserving local data structures. Finally, flow patterns are used to evaluate the recognition performance of flow features. PCA focuses more on identifying the major information in the flow field, while isomap emphasizes identifying more nonlinear information. ICA can mathematically obtain more meaningful independent patterns. In conclusion, each DR algorithm has its own strengths and limitations. Improving evaluation methods to help select the most suitable DR algorithm is more meaningful.