ROBUST UNCERTAINTY QUANTIFICATION USING PRECONDITIONED LEAST-SQUARES POLYNOMIAL APPROXIMATIONS WITH l1-REGULARIZATION - Sorbonne Université Access content directly
Journal Articles International Journal for Uncertainty Quantification Year : 2016

ROBUST UNCERTAINTY QUANTIFICATION USING PRECONDITIONED LEAST-SQUARES POLYNOMIAL APPROXIMATIONS WITH l1-REGULARIZATION

Abstract

We propose a non-iterative robust numerical method for the non-intrusive uncertainty quantification of multivariate stochastic problems with reasonably compressible polynomial representations. The approximation is robust to data outliers or noisy evaluations which do not fall under the regularity assumption of a stochastic truncation error but pertains to a more complete error model, capable of handling interpretations of physical/computational model (or measurement) errors. The method relies on the cross-validation of a pseudospectral projection of the response on generalized Polynomial Chaos approximation bases; this allows an initial model selection and assessment yielding a preconditioned response. We then apply a 1−penalized regression to the preconditioned response variable. Nonlinear test cases have shown this approximation to be more effective in reducing the effect of scattered data outliers than standard compressed sensing techniques and of comparable efficiency to iterated robust regression techniques.
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Dates and versions

hal-01446842 , version 1 (26-01-2017)

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Cite

J W van Langenhove, Didier D Lucor, A Belme. ROBUST UNCERTAINTY QUANTIFICATION USING PRECONDITIONED LEAST-SQUARES POLYNOMIAL APPROXIMATIONS WITH l1-REGULARIZATION. International Journal for Uncertainty Quantification, 2016, 6, pp.57 - 77. ⟨10.1615/Int.J.UncertaintyQuantification.2016015915⟩. ⟨hal-01446842⟩
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