We present a simple and robust strategy for the selection of sampling points in uncertainty quantification. The goal is to achieve the fastest possible convergence in the cumulative distribution function of a stochastic output of interest. We assume that the output of interest is the outcome of a computationally expensive nonlinear mapping of an input random variable, whose probability density function is known. We use a radial function basis to construct an accurate interpolant of the mapping. This strategy enables adding new sampling points one at a time, adaptively. This takes into full account the previous evaluations of the target nonlinear function. We present comparisons with a stochastic collocation method based on the Clenshaw-Curtis quadrature rule, and with an adaptive method based on hierarchical surplus, showing that the new method often results in a large computational saving.

Adaptive sampling, Clenshaw-curtis, Hierarchical surplus
International Journal for Uncertainty Quantification
Modeling DC Circuit-Breakers for Long-Distance Electricity Transmission , Cosmic Lightning
This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/12PR3041-2 - Cosmic Lightning
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Camporeale, E, Agnihotri, A, & Rutjes, C. (2017). Adaptive selection of sampling points for uncertainty quantification. International Journal for Uncertainty Quantification, 7(4), 285–301. doi:10.1615/Int.J.UncertaintyQuantification.2017020027