Knowledge-Driven Dimension Reduction and Reduced Order Surrogate Models

Abstract

This chapter focuses on the knowledge-driven dimension reduction aspect of mechanistic data science. Two types of dimension reduction methods that are introduced in this chapter: clustering and reduced order modeling. Clustering aims to reduce the total number of data points in a dataset by grouping similar data points into clusters. The datapoints within a cluster are considered to be more like each other than datapoints in other clusters. There are multiple methods and algorithms for clustering. In the first part of this chapter, three clustering algorithms are presented, ranging from entry level to advanced level: the Jenks natural breaks, K-means clustering, and self-organizing map (SOM). Clustering is a form of dimension reduction that reduces the total number of data points. In the second part of this chapter, Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) will be introduced as a reduced order modeling technique that reduce the number of features by eliminating redundant and dependent features, leading to a new set of principal features. The resulting model is called a reduced order model. Proper Generalized Decomposition (PGD) is a higher order extension of PCA and will also be introduced.