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

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Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2015, background): “Random selection of regression points has the advantage of being more flexible in selecting the number of required simulations (Eldred et al., 2008).”
Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives] (2013, background): “The or thogonal polynomials for different distribution types can be mixed; see [10] and [11, app.”
Aircraft Robust Trajectory Optimization Using Nonintrusive Polynomial Chaos (2014, background): “In such situations, sparse grid quadrature schemes [26] can be used to enable significant reductions in the computational cost of nonintrusive PC expansions.”
Using Supervised Learning to Improve Monte Carlo Integral Estimation (2011, methodology): “Polynomial chaos methods [5–8] are very effective for small numbers of specific classes of uncertain variables (Gaussian, exponential, uniform, etc.”