Adaptive selection of sampling points for Uncertainty Quantification

TL;DR

This paper introduces an adaptive sampling strategy for Uncertainty Quantification that efficiently converges to the distribution of a stochastic output by sequentially selecting points based on previous evaluations, reducing computational cost.

Contribution

A new adaptive sampling method using radial basis functions for efficient Uncertainty Quantification, outperforming existing stochastic collocation and hierarchical surplus methods.

Findings

Achieves faster convergence in distribution estimation.

Reduces computational cost compared to traditional methods.

Effective for expensive nonlinear models.

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.