Variance-based adaptive sequential sampling for Polynomial Chaos Expansion

This paper presents a novel adaptive sequential sampling method for building Polynomial Chaos Expansion surrogate models. The technique enables one-by-one extension of an experimental design while trying to obtain an optimal sample at each stage of the adaptive sequential surrogate model constructio...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 386; p. 114105
Main Authors: Novák, Lukáš, Vořechovský, Miroslav, Sadílek, Václav, Shields, Michael D.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.12.2021
Elsevier BV
Subjects:
Adaptive sampling
Coherence optimal sampling
Design of experiments
Domains
Hypercubes
Latin hypercube sampling
Microbalances
Model accuracy
Polynomial Chaos Expansion
Polynomials
Sampling methods
Sequential sampling
Coherence optimal sampling
Adaptive sampling
Sequential sampling
Polynomial Chaos Expansion
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:This paper presents a novel adaptive sequential sampling method for building Polynomial Chaos Expansion surrogate models. The technique enables one-by-one extension of an experimental design while trying to obtain an optimal sample at each stage of the adaptive sequential surrogate model construction process. The proposed sequential sampling strategy selects from a pool of candidate points by trying to cover the design domain proportionally to their local variance contribution. The proposed criterion for the sample selection balances both exploitation of the surrogate model and exploration of the design domain. The adaptive sequential sampling technique can be used in tandem with any user-defined sampling method, and here was coupled with commonly used Latin Hypercube Sampling and advanced Coherence D-optimal sampling in order to present its general performance. The obtained numerical results confirm its superiority over standard non-sequential approaches in terms of surrogate model accuracy and estimation of the output variance. •The sequential sampling reflecting the exploration and exploitation is proposed.•The accuracy of results is higher in comparison to non-sequential approach.•The proposed criterion for sequential sampling can be used with any sampling scheme.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114105