{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T18:41:28Z","timestamp":1772131288459,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T00:00:00Z","timestamp":1647820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a15030101","type":"journal-article","created":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T13:24:59Z","timestamp":1647869099000},"page":"101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multi-Fidelity Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Analytical Benchmark Problems"],"prefix":"10.3390","volume":"15","author":[{"given":"Markus P.","family":"Rumpfkeil","sequence":"first","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH 45469, USA"}]},{"given":"Dean","family":"Bryson","sequence":"additional","affiliation":[{"name":"Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA"}]},{"given":"Phil","family":"Beran","sequence":"additional","affiliation":[{"name":"Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Beran, P., Bryson, D., Thelen, A., Diez, M., and Serani, A. 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