Improved metamodels for predicting high-dimensional outputs by accounting for the dependence structure of the latent variables: application to marine flooding

Abstract Metamodelling techniques have shown high performance to overcome the computational burden of numerical hydrodynamic models for fast prediction of key indicators of marine flooding (e.g. total flooded area). To predict flood maps (e.g. spatial distribution of maximum value of water depth during a flood event), a commonly-used approach is to rely on principal component analysis to reduce the high dimensionality of the flood map (related to the number of pixels typically of several 1,000s) by transforming the spatial output into a low number of latent variables (typically <10). One commonly-used approach is to build one metamodel per latent variable by assuming independence between the latent variables. Using two real cases of marine flooding, we show that the predictive performance of the metamodelling approach (relying on kriging metamodels) can significantly be improved when the dependence structure of the latent variables is accounted for. Our tests show that the most efficient approach relies on the clustering in the space of the latent variables (here with k-means algorithm). Complementing the approach with a kriging metamodel specifically dedicated to handle vector-valued variables allows an additional increase of predictability for the case with the larger size of the training dataset.