Nonintrusive least-squares-based polynomial chaos expansion (PCE) techniques have attracted increasing attention among researchers for simple yet efficient surrogate constructions. Different sampling approaches, including optimal design of experiments (DoEs), have been developed to facilitate the least-squares-based PCE construction by reducing the number of required training samples. DoEs mainly include a random selection of the initial sample point and searching a pool of (coherence-optimal) candidate samples to iteratively select the next points based on some optimality criteria. Here, we propose a different way from the common practice to select sample points based on DoEs' optimality criteria, namely backward greedy. The proposed approach starts from a pool of coherence-optimal samples and iteratively removes the most uninfluential sample candidate among a small and randomly selected subset of the pool, instead of the whole pool. Several numerical examples are provided to demonstrate the promises of the proposed approach in improving the accuracy, robustness, and computational efficiency of DoEs. Specifically, it is observed that the proposed backward greedy approach not only improves the computational time for selecting the optimal design but also results in higher approximation accuracy. Most importantly, using the proposed approach, the choice of optimality becomes significantly less critical as different criteria yield similar accuracy when they are used in a backward procedure to select the design points.

中文翻译：

---

通过贪婪向后法提高实验优化设计的准确性和计算效率

基于非侵入性最小二乘的多项式混沌展开（PCE）技术因其简单而有效的替代结构而引起了研究人员越来越多的关注。人们已经开发了不同的采样方法，包括最佳实验设计 (DoE)，通过减少所需的训练样本数量来促进基于最小二乘的 PCE 构建。DoE 主要包括随机选择初始样本点并搜索（相干性最优）候选样本池，以基于某些最优性标准迭代选择下一个点。在这里，我们提出了一种与通常做法不同的方法，即根据 DoE 的最优性标准来选择样本点，即后向贪婪。所提出的方法从相干性最佳样本池开始，并迭代地删除池中随机选择的小子集（而不是整个池）中最具影响力的候选样本。提供了几个数值示例来证明所提出的方法在提高 DoE 的准确性、鲁棒性和计算效率方面的前景。具体来说，我们观察到所提出的后向贪婪方法不仅提高了选择最优设计的计算时间，而且还获得了更高的近似精度。最重要的是，使用所提出的方法，最优性的选择变得不再那么重要，因为当在向后过程中使用不同的标准来选择设计点时，它们会产生相似的精度。