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 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.

翻译：在过去十年中,应用数学和工程学文献中公布了大量用于计算稀有的多盘混乱的算法。我们对现有方法进行了广泛的审查,并制定了算法分类框架。此外,我们还对选择哪些方法在实际应用中最有效使用的方法进行了独特的基准。比较了不同维度和复杂度的若干基准模型的精确度,我们发现,为计算稀有多盘混杂的多盘混杂混杂现象而选择的稀有回归解算法和采样方法可以产生很大差异,在导致的中差差率中可达到几等量。不同的模型维度和实验设计规模体系中,不同方法似乎优于不同的模型维度和实验设计规模。