RT Journal Article ID 2693fddd60c7231d A1 Li, Yiou A1 Anitescu, Mihai A1 Roderick, Oleg A1 Hickernell, Fred T1 ORTHOGONAL BASES FOR POLYNOMIAL REGRESSION WITH DERIVATIVE INFORMATION IN UNCERTAINTY QUANTIFICATION JF International Journal for Uncertainty Quantification JO IJUQ YR 2011 FD 2011-12-02 VO 1 IS 4 SP 297 OP 320 K1 uncertainty quantification K1 representation of uncertainty K1 stochastic collocation K1 heat transfer K1 energy and the environment AB We discuss the choice of polynomial basis for approximation of uncertainty propagation through complex simulation models with capability to output derivative information. Our work is part of a larger research effort in uncertainty quantification using sampling methods augmented with derivative information. The approach has new challenges compared with standard polynomial regression. In particular, we show that a tensor product multivariate orthogonal polynomial basis of an arbitrary degree may no longer be constructed. We provide sufficient conditions for an orthonormal set of this type to exist, a basis for the space it spans. We demonstrate the benefits of the basis in the propagation of material uncertainties through a simplified model of heat transport in a nuclear reactor core. Compared with the tensor product Hermite polynomial basis, the orthogonal basis results in a better numerical conditioning of the regression procedure, a modest improvement in approximation error when basis polynomials are chosen a priori, and a significant improvement when basis polynomials are chosen adaptively, using a stepwise fitting procedure. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,0dc32edb2e7668f2,2693fddd60c7231d.html