Least squares polynomial chaos expansion: A review of sampling strategies
By Mohammad Hadigol, Alireza Doostan. 2017
159 citations recorded by the source corpus.
Abstract As non-intrusive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal, that employs the so-called alphabetic optimality criteria used in the context of ODE in conjunction with coherence-optimal samples. A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE’s, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand. We observed that the alphabetic-coherence-optimal technique outperforms other sampling methods, specially when high-order ODE are employed and/or the oversampling ratio is low.
Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/8014fb21f6fee3f7dc1821391db60c543fce951c
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In Computational Theory and Mathematics
In Management Science and Operations Research
In Statistics and Probability
Citations in the corpus
- Recent advances and applications of surrogate models for finite element method computations: a review (2022, methodology): “A review and a comparison of different sampling strategies for PCE was performed in Hadigol and Doostan (2018).”
- Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems (2018, unknown): “It well-known that the particular sampling strategies for the LSM can dramatically influence the accuracy of the expansion coefficients [14].”