A near-optimal sampling strategy for sparse recovery of polynomial chaos expansions

Highlights: • An algorithm is proposed to identify sample locations in compressive sampling of polynomial expansions. • It does so by improving local-coherence and also cross-correlation properties of measurement matrix. • A greedy algorithm is proposed for the selection of near-optimal locations. • Several numerical examples show accuracy improvement over other sampling strategies. Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations in the parameter space. It was later shown that the choice of sample locations could significantly impact the accuracy of resulting surrogates. This motivated new sampling strategies or design-of-experiment approaches, such as coherence-optimal sampling, which aim at improving the coherence property. In this paper, we propose a sampling strategy that can identify near-optimal sample locations that lead to improvement in local-coherence property and also enhancement of cross-correlation properties of measurement matrices. We provide theoretical motivations for the proposed sampling strategy along with several numerical examples that show that our near-optimal sampling strategy produces substantially more accurate results, compared to other sampling strategies.