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

## TL;DR

This paper introduces a near-optimal sampling strategy for polynomial chaos expansions that improves the accuracy of surrogate models by optimizing sample locations, outperforming existing methods in numerical tests.

## Contribution

It proposes a new sampling strategy that enhances local-coherence and cross-correlation properties, leading to more accurate polynomial chaos surrogates.

## Key findings

- Significantly improves surrogate accuracy over existing sampling methods
- Enhances local-coherence and cross-correlation properties of measurement matrices
- Numerical examples demonstrate superior performance of the proposed strategy

## 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.