Sequential sensitivity analysis of expensive black-box simulators with metamodelling

Simulators are an essential tool in the design and analysis of complex systems. For many tasks in engineering, highly accurate simulators are used instead of expensive real-life experiments. As accuracy increases, these simulators are becoming computationally more expensive to evaluate. Sensitivity analysis provides information on the importance of the inputs with regard to the outputs. This does not only provide critical information about the workings of the system but also allows to discard inputs with low impact on the outputs. However, sensitivity analysis is an expensive process in terms of number of evaluations. Hence, metamodelling techniques are used to reduce the computational burden. In this paper we present, discuss and evaluate a novel algorithm for sequential variance-based and derivative-based sensitivity analysis of expensive black-box simulators using metamodelling. Two new stopping criteria are proposed on top of the traditional model error based stopping criteria. Extensive testing on benchmark problems and engineering use cases shows the sensitivity indices can be efficiently and accurately computed with a limited number of simulator evaluations.