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

Siham El Garroussi,Sophie Ricci,Didier Lucor,Matthias De Lozzo,Nicole Goutal

doi:10.1007/s00477-021-02060-7

Abstract

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.

Highlights

1.1 Flood monitoringAccording to the World Health Organization (WHO), in Europe, floods are the most common natural hazard leading3 edf-R&D/LHSV, 6 Quai Watier, 78401 Chatou, France 4 CNRS, Laboratoire Interdisciplinaire des Sciences du Numerique, Universite Paris-Saclay, Orsay, France to emergencies, causing extensive damage, disruption and health effects (WHO 2017)
For the sake of simplicity, we focus on a mono-dimensional output variable y
The size of the latent space p~ is plotted along the x-axis, the left y-axis represents the Root Mean Squared Error (RMSE) in meters for PCA and AE, and the right y-axis represents the cumulated explained variance for the PCA

Summary

Introduction

1.1 Flood monitoringAccording to the World Health Organization (WHO), in Europe, floods are the most common natural hazard leading3 edf-R&D/LHSV, 6 Quai Watier, 78401 Chatou, France 4 CNRS, Laboratoire Interdisciplinaire des Sciences du Numerique, Universite Paris-Saclay, Orsay, France to emergencies, causing extensive damage, disruption and health effects (WHO 2017). Resilient and proactive health systems that anticipate needs and challenges are more likely to reduce risks and respond effectively during emergencies, thereby saving lives and alleviating human suffering. In this sense, several measures have been taken. This section proposes a reduced Mixture of Polynomial Chaos Expansions (rMPCE) This advanced surrogate model strategy aims to predict a 2D output field subject to non-linearities with respect to sub-divided input space variables. This strategy features an output reduction stage and a local regression stage via clustering and classification. The corresponding learning input matrix is denoted X with 1⁄2Xij 1⁄4 xðjiÞ and the learning output matrix is denoted Y with

Methods

Results

Conclusion