RT Journal Article ID 3261384c6ba6c1c2 A1 Van Langenhove, Jan A1 Lucor, D. A1 Belme, A. T1 ROBUST UNCERTAINTY QUANTIFICATION USING PRECONDITIONED LEAST-SQUARES POLYNOMIAL APPROXIMATIONS WITH l1-REGULARIZATION JF International Journal for Uncertainty Quantification JO IJUQ YR 2016 FD 2016-08-16 VO 6 IS 1 SP 57 OP 77 K1 uncertainty quantification K1 polynomial chaos K1 robust regression K1 outliers K1 model validation and verification K1 compressed sensing K1 weighted least squares K1 l1-minimization AB 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. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,6695b1fe0a01e538,3261384c6ba6c1c2.html