Functional principal component analysis for global sensitivity analysis of model with spatial output
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Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three main issues. First, due to computational time, standard SA techniques cannot be directly applied on the simulator. Second, the output is infinite dimensional, or at least high dimensional if the output is discretized. Third, the spatial output is non-stationary and exhibits strong local variations. We show that all these issues can be addressed all together by using functional PCA (FPCA). In contrast to the RKHS view of FPCA, we first specify a functional basis, such as wavelets or B-splines, designed to handle local variations. Secondly, FPCA reduces dimension by doing PCA on the basis coefficients with an ad-hoc metric. Finally, fast-to-evaluate metamodels are built on the few selected principal components. They provide a proxy on which SA can be done. As a by-product, we obtain analytical formulas for variance-based sensitivity indices, generalizing known formula assuming orthonormality of basis functions.
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