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A Reduced-Basis Polynomial-Chaos Approach with a Multi-parametric Truncation Scheme for Problems with Uncertainties

In: Approximation Theory and Analytic Inequalities

Author

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  • Theodoros T. Zygiridis

    (University of Western Macedonia, Department of Electrical and Computer Engineering)

Abstract

Polynomial-chaos (PC) expansions constitute an invaluable tool for the investigation of uncertainty quantification problems, yet minimizing the consequences of the so-called curse of dimensionality requires methodologies that ensure reliable performance with a set of basis functions with reduced cardinality. In this work, we propose the construction of the PC basis set using a multi-parametric truncation scheme that generalizes standard ones and enables the derivation of anisotropic surrogates in a flexible fashion. The specification of the truncation rule’s design parameters relies on a preliminary variance analysis, which entails only a fraction of the overall computational cost and enables a sufficient screening of the input variables. Despite its simplicity, the proposed approach is capable of deriving as credible results as the original PC method with fewer basis functions, due to the elimination of unnecessary terms, thus providing a more efficient framework for the study of demanding stochastic problems.

Suggested Citation

  • Theodoros T. Zygiridis, 2021. "A Reduced-Basis Polynomial-Chaos Approach with a Multi-parametric Truncation Scheme for Problems with Uncertainties," Springer Books, in: Themistocles M. Rassias (ed.), Approximation Theory and Analytic Inequalities, pages 529-546, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-60622-0_26
    DOI: 10.1007/978-3-030-60622-0_26
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