论文标题
稀疏多项式混乱扩展：文献调查和基准测试
Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
论文作者
论文摘要
稀疏的多项式混乱扩展（PCE）是一种流行的替代建模方法，它利用PCE的性质，效应原理的稀疏性和强大的稀疏回归求解器，以近似具有许多输入参数的计算机模型，仅依赖于少数模型评估。在过去的十年中，已在应用数学和工程文献中发表了大量用于计算稀疏PCE的算法。我们对现有方法进行了广泛的审查，并开发了分类算法的框架。此外，我们对选择哪种方法在实际应用中效果最好的方法进行了独特的基准。将它们在不同维度和复杂性的几种基准模型上进行比较，我们发现稀疏回归求解器和用于计算稀疏PCE替代物的采样方案的选择可以产生显着差异，在产生的均值误差中多达几个数量级。在模型维度和实验设计尺寸的不同制度中，不同的方法似乎是优越的。
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.
