SIAM/ASA Journal on Uncertainty Quantification, Volume 9, Issue 2, Page 593-649, January 2021.
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with many input parameters, relying on only a few model evaluations. Within the last decade, a large number of algorithms for the computation of sparse PCE have been published in the applied math and engineering literature. We present an extensive review of the existing methods and develop a framework for classifying the algorithms. Furthermore, we conduct a unique benchmark on a selection of methods to identify which approaches work best in practical applications. Comparing their accuracy on several benchmark models of varying dimensionality and complexity, we find that the choice of sparse regression solver and sampling scheme for the computation of a sparse PCE surrogate can make a significant difference of up to several orders of magnitude in the resulting mean-squared error. Different methods seem to be superior in different regimes of model dimensionality and experimental design size.

中文翻译：

---

稀疏多项式混沌扩展：文献调查和基准

SIAM / ASA不确定性量化杂志，第9卷，第2期，第593-649页，2021年1月
稀疏多项式混沌展开（PCE）是一种流行的替代建模方法，该方法利用PCE的特性，稀疏效应原理和强大的稀疏回归求解器来近似仅具有少数几个输入参数的计算机模型评估。在过去的十年中，在应用数学和工程文献中已经发布了许多用于计算稀疏PCE的算法。我们对现有方法进行了广泛的回顾，并开发了用于对算法进行分类的框架。此外，我们针对各种方法进行了独特的基准测试，以确定哪种方法在实际应用中最有效。在不同维度和复杂度的几种基准模型上比较它们的准确性，我们发现，选择稀疏回归求解器和抽样方案来计算稀疏PCE替代项可以在产生的均方误差中产生高达几个数量级的显着差异。在不同的模型尺寸和实验设计尺寸方面，不同的方法似乎更为优越。