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

Metamodelling techniques (also referred to as surrogate modelling) 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 1000 s) 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, but only if two conditions are jointly met: (1) the number of training samples is sufficiently high to learn the dependence structure over the respective clusters; (2) a careful selection of the number of clusters has been performed.

Automated summary

Metamodelling techniques can help overcome the computational burden of numerical hydrodynamic models for fast prediction of marine flooding indicators. A commonly-used approach is to reduce the dimensionality of flood maps using principal component analysis and build independent metamodels for each latent variable. However, considering the dependence structure of latent variables and clustering in their space can significantly improve the predictive performance. Using a kriging metamodel specifically designed for vector-valued variables can further enhance predictability, given a sufficient number of training samples and careful selection of clusters.