Global sensitivity analysis for computationally expensive models based on radial basis function interpolationand optimization

We present a surrogate and optimization-assisted global sensitivity analysis framework for multimodal and computationally expensive “black box” objective functions f(x), which could be a simulation or computer code. A surrogate surfaces (x) based on an affordable number of evaluations of f(x) creates an approximation of f(x) for all x. The evaluation-intensive global sensitivity analysis (Extended FAST) is performed on s(x). We compare 4 algorithms including a) optimization plus RBF surrogate, b) optimization plus polynomial regression surrogate, c) RBF based on Latin Hypercube Design (LHD) with no optimization, and d) conventional application of Extended FAST global optimization (with no surrogate). In cases a) and b) the optimization points are supplemented with LHD evaluations. In all cases a) (which is an algorithm called SA_SO_GRBF) substantially outperformed the alternatives by having the smallest error on both total global sensitivity (with parameter interactions) and first order sensitivity (without parameter interaction).