A Near-Optimal Sampling Strategy for Sparse Recovery of Polynomial Chaos Expansions

Abstract

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.

References in corpus (3)

• Compressive Sampling of Polynomial Chaos Expansions: Convergence Analysis and Sampling Strategies
• A generalized sampling and preconditioning scheme for sparse approximation of polynomial chaos expansions
• Divide and Conquer: An Incremental Sparsity Promoting Compressive Sampling Approach for Polynomial Chaos Expansions

Cited by in corpus (5)

• Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
• Sparse Polynomial Chaos Expansions via Compressed Sensing and D-optimal Design
• Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization
• A preconditioning approach for improved estimation of sparse polynomial chaos expansions
• Sliced-Inverse-Regression-Aided Rotated Compressive Sensing Method for Uncertainty Quantification