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International Journal for Uncertainty Quantification
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ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2016015915
pages 57-77

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

Jan Van Langenhove
Sorbonne Universités, UPMC Univ Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France; CNRS, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France
D. Lucor
LIMSI, CNRS, Université Paris-Saclay, Campus Universitaire bat 508, Rue John von Neumann, F-91405 Orsay cedex, France
A. Belme
Sorbonne Universités, UPMC Univ Paris 06, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France; CNRS, UMR 7190, Institut Jean le Rond d'Alembert, F-75005, Paris, France

RÉSUMÉ

We propose a noniterative robust numerical method for the nonintrusive 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 l1-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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