This thesis contributions belong to the general framework of data-based and physically- based data-driven modelling. An efficient approach for Machine Learning (ML), as well as a speed-up technique for Data Assimilation (DA), have been developed. For this purpose, Dimensionality Reduction (DR) and stochastic spectral modelling were used. In particular, a coupling between Proper Orthogonal Decomposition (POD) and Polynomial Chaos Expansion (PCE) is at the center of this thesis contributions.
POD and PCE have widely proved their worth in their respective frameworks, and the idea was to combine them for optimal field measurement based forecasting, and ensemble- based acceleration technique for variational DA. For this purpose, (i) a physically inter- pretable POD-PCE ML for non-linear multidimensional fields was developed in the Neural Networks (NN) paradigm and (ii) a hybrid ensemble-variational DA approach for para- metric calibration was proposed with adapted calculations of POD-PCE metamodelling error covariance matrix.
The proposed techniques were assessed in the context of an industrial application, for the study of sedimentation in a coastal power plant's water intake. Water intakes ensure plant cooling via a pumping system. They can be subject to sediment accumulation, which represents a clogging risk and requires costly dredging operations. For monitoring and safety reasons, the power plant stakeholders asked for a predictive tool that could be run in operational conditions. Data collected during many years of monitoring in the study area were provided. The objective was then to achieve comprehensive analysis of the flow and sediment dynamics, as well as to develop an optimal model in terms of forecasting accuracy, physical meaning, and required computational time. Uncertainty reduction and computational efficiency were therefore starting points for all proposed contributions.
In addition to the previously proposed methods, Uncertainty Quantificiation (UQ) studies were undertaken. Specifically, (i) uncertainties related to tidal hydrodynamic modelling, resulting from common modelling choices (domain size, empirical closures) were investigated. POD patterns resulting from measurements and numerical scenarios were compared; (ii) UQ study of the sediment transport modelling in the intake, in a high- dimensional framework, was achieved. Investigations were based on appropriate DR. In fact, POD patterns of Boundary Conditions (BC) and Initial Conditions (IC), resulting from hydrodynamic simulations outputs and from bathymetry measurements respectively, were used.
A perspective of this work would be to implement a hybrid POD-PCE model, using both measured and numerically emulated data, to better understand and predict complex physical processes. This approach would offer a complete, fast and efficient tool for operational predictions.
data-based prediction, physically-based data-driven modelling, statistical learning, data assimilation, uncertainty quantification, sensitivity analysis, geosciences, hydrodynamics, sediment transport, coastal intake.
Olivier Le Maitre, Professeur des Universités, Centre de Mathématiques Appliquées of the École Polytechnique (CMAP) (Rapporteur)
Pierre-Olivier Malaterre, Chercheur, INRAE Montpellier (Rapporteur)
Clémentine Prieur, Professeure des Universités, Université Grenoble Alpes, (Examinatrice)
Christine Keribin, Maître de conférences, Université Paris-Sud, (Examinatrice)
Hélène Roux, Maître de conférences, IMFT, (Examinatrice)
Florent Lyard, Professeur des Universités, LEGOS (Examinateur)
Olivier Thual, Professeur des Universités, Institut National Polytechnique de Toulouse (Directeur de thèse)
Cédric Goeury, Ingénieur-Chercheur, EDF R&D LNHE (encadrant principal)
Fabrice Zaoui, Ingénieur-Chercheur, EDF R&D LNHE (encadrant)
Pablo Tassi, Ingénieur-Chercheur, EDF R&D LNHE (encadrant)