Functional principal component analysis for global sensitivity analysis of model with spatial output

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 input parameters on There are three main issues. First, due computational time, standard SA techniques cannot be directly applied simulator. Second, output infinite dimensional, or at least high dimensional if discretized. Third, non-stationary and exhibits strong local variations. We show that all these issues can addressed together using functional PCA (FPCA). first specify basis, such as wavelets B-splines, designed handle Secondly, select most influential basis terms, either an energy criterion after orthonormalization, original penalized regression approach. Then FPCA further reduces dimension doing coefficients, ad-hoc metric. Finally, fast-to-evaluate metamodels built few selected principal components. They provide proxy which done. As by-product, obtain analytical formulas for variance-based indices, generalizing known formula assuming orthonormality functions.