Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos.

Polynomial chaos expansions (PCE) are an attractive technique for uncertainty quantification (UQ) due to their strong mathematical basis and ability to produce functional representations of stochastic variability. When tailoring the orthogonal polynomial bases to match the forms of the input uncertainties in a Wiener-Askey scheme, excellent convergence properties can be achieved for general probabilistic analysis problems. Non-intrusive PCE methods allow the use of simulations as black boxes within UQ studies, and involve the calculation of chaos expansion coefficients based on a set of response function evaluations. These methods may be characterized as being either Galerkin projection methods, using sampling or numerical integration, or regression approaches (also known as point collocation or stochastic response surfaces), using linear least squares. Numerical integration methods may be further categorized as either tensor product quadrature or sparse grid Smolyak cubature and as either isotropic or anisotropic. Experience with these approaches is presented for algebraic and PDE-based benchmark test problems, demonstrating the need for accurate, efficient coefficient estimation approaches that sca le for problems with significant numbers of random variables.