Tackling random fields non-linearities with unsupervised clustering of polynomial chaos expansion in latent space: application to global sensitivity analysis of river flooding

A surrogate model is developed to accurately approximate a two-dimensional hydrodynamics numerical solver in order to conduct a reduced-cost variance-based global sensitivity analysis of the hydraulic state. The impact of uncertainties in river bottom friction and boundary conditions on the simulated water depth is analyzed for quasi-unsteady flows. An autoencoder technique adapted to non-linear variable dimension reduction is used to reduce the multi-dimensional model output so that the formulation of the surrogate remains computationally parsimonious. In addition, following the divide-and-conquer principle, a mixture of local polynomial chaos expansions is proposed to deal with non-linearity in the hydraulic state with respect to uncertain inputs. Machine learning techniques are used to automatically partition the input space into clusters that are not affected by non-linearities and support accurate surrogates. This combined strategy is applied to a reach of the Garonne River where river and floodplains dynamics are simulated by the numerical solver Telemac-2D. The merits of this strategy are highlighted when the flood front reaches regions where the topography features a strong gradient and where, consequently, strong non-linearities occur between the water depth and friction as well as hydrologic input forcing. By applying this strategy, the $$Q_2$$ metric improves by 90% compared to a classical polynomial chaos expansion surrogate, resulting in a much more reliable sensitivity analysis. This is particularly important in floodplain areas where human and economic activities are at stake.