This paper proposes a new deterministic sampling strategy for constructingpolynomial chaos approximations for expensive physics simulation models. Theproposed approach, effectively subsampled quadratures involves sparselysubsampling an existing tensor grid using QR column pivoting. For polynomialinterpolation using hyperbolic or total order sets, we then solve the followingsquare least squares problem. For polynomial approximation, we use a columnpruning heuristic that removes columns based on the highest total orders andthen solves the tall least squares problem. While we provide bounds on thecondition number of such tall submatrices, it is difficult to ascertain howcolumn pruning effects solution accuracy as this is problem specific. Weconclude with numerical experiments on an analytical function and a modelpiston problem that show the efficacy of our approach compared with randomizedsubsampling. We also show an example where this method fails.
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