Optimal space-filling design for symmetrical global sensitivity analysis of complex black-box models

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 ϕ_q and L₂-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.