Dimensionality Reduction in Surrogate Modeling: A Review of Combined Methods

• Published in: Data Science and Engineering Vol. 7; no. 4; pp. 402 - 427
• Main Authors: Hou, Chun Kit Jeffery, Behdinan, Kamran
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.12.2022; Springer; Springer Nature B.V
• Subjects: Accuracy; Algorithm Analysis and Problem Complexity; Algorithms; Artificial Intelligence; Chemistry and Earth Sciences; Complexity; Computer Science; Data mining; Data Mining and Knowledge Discovery; Database Management; Datasets; Discriminant analysis; Efficiency; Eigenvalues; Eigenvectors; Engineering; Feature extraction; Feature selection; Investigations; Linear algebra; Literature reviews; Machine learning; Nonlinear phenomena; Physics; Principal components analysis; Reduction; Review/Survey Papers; Scale models; State-of-the-art reviews; Statistics for Engineering; Systems and Data Security; Canada; Dimensionality reduction; High dimensionality; Surrogate modeling; Neural networks; Machine learning
• ISSN: 2364-1185; 2364-1541; 2364-1541
• DOI: 10.1007/s41019-022-00193-5

Surrogate modeling has been popularized as an alternative to full-scale models in complex engineering processes such as manufacturing and computer-assisted engineering. The modeling demand exponentially increases with complexity and number of system parameters, which consequently requires higher-dimensional engineering solving techniques. This is known as the curse of dimensionality. Surrogate models are commonly used to replace costly computational simulations and modeling of complex geometries. However, an ongoing challenge is to reduce execution and memory consumption of high-complexity processes, which often exhibit nonlinear phenomena. Dimensionality reduction algorithms have been employed for feature extraction, selection, and elimination for simplifying surrogate models of high-dimensional problems. By applying dimensionality reduction to surrogate models, less computation is required to generate surrogate model parts while retaining sufficient representation accuracy of the full process. This paper aims to review the current literature on dimensionality reduction integrated with surrogate modeling methods. A review of the current state-of-the-art dimensionality reduction and surrogate modeling methods is introduced with a discussion of their mathematical implications, applications, and limitations. Finally, current studies that combine the two topics are discussed and avenues of further research are presented.