Non-linear data-driven modelling on multidimensional fields : an application to hydro-morphodynamic coastal flows

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 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 interpretable 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 parametric 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 Quantification (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 highdimensional 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

Sensitivity of tidal modelling in coastal configurations: an uncertainty study based on field-measurement reduction

Hydrodynamic

Modélisation non-linéaire de champs multidimensionnels guidée par la donnée : application aux écoulements côtiers hydromorphodynamiques

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 interpretable 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 parametric 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 highdimensional framework, was achieved. Investigations were based on appropriate DR. Infact, 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.Les contributions de cette thèse figurent dans le cadre général de la modélisation à base de données et des approches physiques guidées par des données. Une méthode d'apprentissage statistique, ainsi qu'une technique d'accélération pour l'Assimilation de Données (AD), ont été développées. Pour cela, la Réduction de Dimension et la modélisation stochastique spectrale sont utilisées. En particulier, un couplage entre Décomposition en modes Propres Orthogonaux (POD) et Expansion par Polynômes du Chaos (PCE), est au centre des différentes contributions. Les techniques POD et PCE sont toutes deux largement reconnues. L'idée ici estde les combiner pour mettre en place une prédiction optimale à base de données de mesures, et accélérer les techniques d'Assimilation de Données variationnelle sur la base d'une approche d'ensemble. Pour cela, (i) un modèle de Machine Learning POD-PCE, interprétable physiquement, et adapté aux champs multidimensionnels non-linéaires, a été développé dans un paradigme de Réseaux de Neurones et (ii) une approche ensembliste variationnelle hybride d'AD, pour la calibration paramétrique a été proposée, avec un calcul adapté de la matrice de covariance d'erreur du métamodèle POD-PCE. Les approches proposées ont été motivées par une problématique industrielle, avec une question physique complexe : la sédimentation dans un chenal d'amenée bord-de-merd'une centrale électrique. Les chenaux d'amenée assurent le refroidissement des centrales à travers un système de pompage. Ils peuvent être sujets à une accumulation de sédiments, ce qui représente un risque de colmatage et requiert des opérations de dragage coûteuses. Pour des raisons de gestion et de sécurité, l'industriel opérant la centrale d'intérêt demande un outil prédictif pour des conditions opérationnelles. Les données collectées durant plusieurs années de gestion ont été fournies. L'objectif est d'analyser la dynamique observée, ainsi que de développer un modèle optimal, à la fois prédictif, physiquement interprétable, et à coût de calcul limité. La réduction de l'incertitude et la diminution du temps de simulation ont donc été un point de départ pour toutes les contributions proposées. En supplément des méthodes citées précédemment, des études de Quantification d'Incertitudes (UQ) ont été menées. Plus précisément, (i) les incertitudes liées à la modélisation hydrodynamique de la marée, résultant de choix de modélisation communs (taille de domaine, lois empiriques), ont été investiguées. Les motifs POD des mesures et des scénarios numériques ont été comparés ; (ii) l'étude UQ de la modélisation du transport sédimentaire dans le chenal, dans un cadre à haute-dimension, a été réalisée. Les investigations se sont basées sur une Réduction de Dimension appropriée. En effet, les motifs POD des Conditions aux Limites, et ceux des Conditions Initiales, résultant de simulations hydrodynamiques et de mesures bathymétriques respectivement, ont été utilisées. Une perspective de ce travail serait d'implémenter un modèle POD-PCE hybride, utilisant à la fois des données de mesures et des données simulées numériquement, pourmieux comprendre et prédire des processus physiques complexes. Cette approche offrirait un outil complet, rapide et efficace pour des prédictions opérationnelles

Physically interpretable machine learning algorithm on multidimensional non-linear fields

International audienceIn an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE), widely used in the Uncertainty Quantification community (UQ), has long been employed as a robust representation for probabilistic input-to-output mapping. It has been recently tested in a pure ML context, and shown to be as powerful as classical ML techniques for point-wise prediction. Some advantages are inherent to the method, such as its explicitness and adaptability to small training sets, in addition to the associated probabilistic framework. Simultaneously, Dimensionality Reduction (DR) techniques are increasingly used for pattern recognition and data compression and have gained interest due to improved data quality. In this study, the interest of Proper Orthogonal Decomposition (POD) for the construction of a statistical predictive model is demonstrated. Both POD and PCE have amply proved their worth in their respective frameworks. The goal of the present paper was to combine them for a field-measurement-based forecasting. The described steps are also useful to analyze the data. Some challenging issues encountered when using multidimensional field measurements are addressed, for example when dealing with few data. The POD-PCE coupling methodology is presented, with particular focus on input data characteristics and training-set choice. A simple methodology for evaluating the importance of each physical parameter is proposed for the PCE model and extended to the POD-PCE coupling