In this paper, a novel concept of optimal space-filling identifiable design is proposed in the framework of symmetrical global sensitivity analysis for exploring complex black-box models. The initial identifiable design is first generated algorithmically. Then based on two commonly used measures of space filling, the ${\varphi }_q$ and $L_2$-discrepancy criterions, two optimal space-filling identifiable designs are proposed. The corresponding optimization algorithms are also given, in which adjacent identifiable designs are produced sequentially by using track substitution until the space-filling property has been optimized. By using the resulting optimal space-filling identifiable design, symmetrical global sensitivity indices can be directly estimated based on model outputs with high precision. Extensive theoretical and numerical results demonstrate the optimality and effectiveness of the proposed designs, as well as the superiority over the existing designs in the literature. Technical details are provided in the Appendix.

在本文中，在对称全局灵敏度分析的框架下，提出了一种新的最优空间填充可识别设计概念，用于探索复杂的黑盒模型。最初的可识别设计首先通过算法生成。然后基于两种常用的空间填充措施，${\phi }_q$ 和 ${升}_2$-差异标准，提出了两种最佳空间填充可识别设计。还给出了相应的优化算法，其中相邻的可识别设计通过使用轨道替换顺序产生，直到空间填充特性得到优化。通过使用得到的最优空间填充可识别设计，可以根据模型输出高精度直接估计对称全局敏感度指标。大量的理论和数值结果证明了所提出设计的最优性和有效性，以及优于文献中现有设计的优势。技术细节在附录中提供。