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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2017020027
pages 285-301

ADAPTIVE SELECTION OF SAMPLING POINTS FOR UNCERTAINTY QUANTIFICATION

Enrico Camporeale
Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands
Ashutosh Agnihotri
Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands
Casper Rutjes
Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands

ABSTRACT

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.