Multi-Fidelity Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Analytical Benchmark Problems

• Published in: Algorithms Vol. 15; no. 3; p. 101
• Main Authors: Rumpfkeil, Markus P., Bryson, Dean, Beran, Phil
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2022
• Subjects: Accuracy; Algorithms; analytical benchmark problems; Approximation; Benchmarks; Computing costs; Design optimization; Functions (mathematics); kriging; Mathematical analysis; multi-fidelity surrogate models; Optimization; Polynomials; sparse polynomial chaos expansions; Sparsity; Trends
• ISSN: 1999-4893; 1999-4893
• DOI: 10.3390/a15030101

In this article, multi-fidelity kriging and sparse polynomial chaos expansion (SPCE) surrogate models are constructed. In addition, a novel combination of the two surrogate approaches into a multi-fidelity SPCE-Kriging model will be presented. Accurate surrogate models, once obtained, can be employed for evaluating a large number of designs for uncertainty quantification, optimization, or design space exploration. Analytical benchmark problems are used to show that accurate multi-fidelity surrogate models can be obtained at lower computational cost than high-fidelity models. The benchmarks include non-polynomial and polynomial functions of various input dimensions, lower dimensional heterogeneous non-polynomial functions, as well as a coupled spring-mass-system. Overall, multi-fidelity models are more accurate than high-fidelity ones for the same cost, especially when only a few high-fidelity training points are employed. Full-order PCEs tend to be a factor of two or so worse than SPCES in terms of overall accuracy. The combination of the two approaches into the SPCE-Kriging model leads to a more accurate and flexible method overall.