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Renard, Philippe
Nom
Renard, Philippe
Affiliation principale
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Directeur de Recherche
Email
Philippe.Renard@unine.ch
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Voici les éléments 1 - 6 sur 6
- PublicationAccès libreIce volume and basal topography estimation using geostatistical methods and GPR measurements: Application on the Tsanfleuron and Scex Rouge glacier, Swiss Alps(2021-7)
; ; ; ; Ground Penetrating Radar (GPR) is nowadays widely used for determining glacier thickness. However, this method provides thickness data only along the acquisition lines and therefore interpolation has to be made between them. Depending on the interpolation strategy, calculated ice volumes can differ and can lack an accurate error estimation. Furthermore, glacial basal topography is often characterized by complex geomorphological features, which can be hard to reproduce using classical 5 interpolation methods, especially when the conditioning data are sparse or when the morphological features are too complex. This study investigates the applicability of multiple-point statistics (MPS) simulations to interpolate glacier bedrock topography using GPR measurements. In 2018, a dense GPR data set was acquired on the Tsanfleuron Glacier (Switzerland). The results obtained with the direct sampling MPS method are compared against those obtained with kriging and sequential Gaussian simulations (SGS) on both a synthetic data set – with known reference volume and bedrock topography – and the real data 10 underlying the Tsanfleuron glacier. Using the MPS modelled bedrock, the ice volume for the Scex Rouge and Tsanfleuron Glacier is estimated to be 113.9 ± 1.6 Miom3 . The direct sampling approach, unlike the SGS and the kriging, allowed not only an accurate volume estimation but also the generation of a set of realistic bedrock simulations. The complex karstic geomorphological features are reproduced, and can be used to significantly improve for example the precision of under-glacial flow estimation. - PublicationAccès libreAn Attempt to Boost Posterior Population Expansion Using Fast Machine Learning Algorithms(2021-3)
; In hydrogeology, inverse techniques have become indispensable to characterize subsurface parameters and their uncertainty. When modeling heterogeneous, geologically realistic discrete model spaces, such as categorical fields, Monte Carlo methods are needed to properly sample the solution space. Inversion algorithms use a forward operator, such as a numerical groundwater solver. The forward operator often represents the bottleneck for the high computational cost of the Monte Carlo sampling schemes. Even if efficient sampling methods (for example Posterior Population Expansion, PoPEx) have been developed, they need significant computing resources. It is therefore desirable to speed up such methods. As only a few models generated by the sampler have a significant likelihood, we propose to predict the significance of generated models by means of machine learning. Only models labeled as significant are passed to the forward solver, otherwise, they are rejected. This work compares the performance of AdaBoost, Random Forest, and convolutional neural network as classifiers integrated with the PoPEx framework. During initial iterations of the algorithm, the forward solver is always executed and subsurface models along with the likelihoods are stored. Then, the machine learning schemes are trained on the available data. We demonstrate the technique using a simulation of a tracer test in a fluvial aquifer. The geology is modeled by the multiple-point statistical approach, the field contains four geological facies, with associated permeability, porosity, and specific storage values. MODFLOW is used for groundwater flow and transport simulation. The solution of the inverse problem is used to estimate the 10 days protection zone around the pumping well. The estimated speed-ups with Random Forest and AdaBoost were higher than with the convolutional neural network. To validate the approach, computing times of inversion without and with machine learning schemes were computed and the error against the reference solution was calculated. For the same mean error, accelerated PoPEx achieved a speed-up rate of up to 2 with respect to the standard PoPEx. - PublicationAccès libreA Framework for the Cross‐Validation of Categorical Geostatistical Simulations(2020-6)
; ; The mapping of subsurface parameters and the quantification of spatial uncertainty requires selecting adequate models and their parameters. Cross‐validation techniques have been widely used for geostatistical model selection for continuous variables, but the situation is different for categorical variables. In these cases, cross‐validation is seldom applied, and there is no clear consensus on which method to employ. Therefore, this paper proposes a systematic framework for the cross‐validation of geostatistical simulations of categorical variables such as geological facies. The method is based on K‐fold cross‐validation combined with a proper scoring rule. It can be applied whenever an observation data set is available. At each cross‐validation iteration, the training set becomes conditioning data for the tested geostatistical model, and the ensemble of simulations is compared to true values. The proposed framework is generic. Its application is illustrated with two examples using multiple‐point statistics simulations. In the first test case, the aim is to identify a training image from a given data set. In the second test case, the aim is to identify the parameters in a situation including nonstationarity for a coastal alluvial aquifer in the south of France. Cross‐validation scores are used as metrics of model performance and quadratic scoring rule, zero‐one score, and balanced linear score are compared. The study shows that the proposed fivefold stratified cross‐validation with the quadratic scoring rule allows ranking the geostatistical models and helps to identify the proper parameters. - PublicationAccès libreConditioning Multi-Gaussian Groundwater Flow Parameters to Transient Hydraulic Head and Flowrate Data With Iterative Ensemble Smoothers: A Synthetic Case Study(2020-6)
; ; ; - PublicationAccès libreUsing Generative Adversarial Networks as a Fast Forward Operator for Hydrogeological Inverse Problems(2020-4)
; Subsurface characterization using inverse techniques constitutes one of the fundamental elements of hydrogeological modeling applications. Available methods to solve inverse problems rely on a forward operator that predicts state variables for a given set of subsurface parameters. As the number of model parameters to be estimated increases, forward operations incur a significant computational demand. In this paper, we investigate the use of conditional generative adversarial networks (cGAN) as an emulator for the forward operator in the context of a hydrogeological inverse problem. We particularly investigate if the cGAN can be used to replace the forward operator used in the adaptive importance sampling method posterior population expansion (PoPEx) with reasonable accuracy and feasible computation requirement. The cGAN model trained on channelized geological structures has shown that the cGAN is able to reproduce the state variables corresponding to a certain parameter field. Hence, its integration in PoPEx yielded satisfactory results. In terms of the computational demand, the use of cGAN as a surrogate forward model reduces the required computational time up to 80% for the problem defined in the study. However, the training time required to create a model seems to be the major drawback of the method. - PublicationAccès libreConditioning groundwater flow parameters with iterative ensemble smoothers: analysis and approaches in the continuous and the discrete cases(2020)
; ; L’assimilation de données consiste à combiner de façon optimale les observations (données) et les prévisions produites par un modèle numérique d’un système dynamique étudié. Au cours de la dernière décennie, les méthodes basées sur le filtre de Kalman d’ensemble (EnKF) pour l’assimilation de données ont été particulièrement explorées dans diverses disciplines des géosciences pour résoudre des problèmes inverses. Bien que ces méthodes d’ensemble aient été développées afin de pouvoir traiter efficacement des problèmes de grandes dimensions, elles supposent que les erreurs qui affectent les observations et le modèle suivent une loi de distribution Gaussienne multivariée. Pour traiter de potentielles nonlinéarités entre les données et les variables paramètres ou d’état que l’on souhaite conditionner, des variantes itératives de méthodes existantes ont été proposées. Dans cette thèse, nous nous intéressons dans un premier temps à la performance de deux principales méthodes de lisseur d’ensemble itératif pour le calage d’un modèle synthétique d’écoulement souterrain 2D. A partir du même jeu de données ponctuelles (locales) et transitoires (dynamiques), nous analysons la performance de chaque méthode pour le conditionnement d’un ensemble de champs multi-Gaussiens de valeurs de conductivité hydraulique. Nous explorons ensuite plus particulièrement l’application d’une des méthodes, ES-MDA, dans des situations plus ou moins complexes suivant la méthode de simulation géostatistique employée pour représenter l’information géologique a priori. Nous évaluons tout d’abord la pertinence d’une paramétrisation basée sur une transformation normal-score dans un cas non-multi-Gaussien. La robustesse de la méthode d’ensemble face aux nonlinéarités est ensuite plus particulièrement testée dans le cas de réalisations de variables discrètes de facies géologique obtenues par la technique des gaussiennes tronquées et mises à jour via leurs variables continues sous-jacentes. En nous basant sur les limitations et avantages observées expérimentalement pour les paramétrisations précédemment évoquées, nous proposons finalement une nouvelle méthodologie d’assimilation de données dynamiques. Bien qu’elle implique une méthode classique de Kalman d’ensemble, la méthodologie proposée permet spécifiquement le conditionnement de champs de facies géologiques, soit de variables discrètes, qui sont initialement simulés par statistiques à points multiples (MPS). Cette méthodologie s’appuie sur une paramétrisation multi-résolutions nouvelle de la simulation MPS catégorique où, l’ensemble de paramètres latents est défini initialement à partir des simulations à l’échelle la plus grossière d’un ensemble de simulations MPS multi-résolutions. Comme cet ensemble n’est pas multi-Gaussien, des étapes additionnelles précédant le calcul de la première correction sont proposées. Notamment, les paramètres sont corrigés à des points prédéfinis à l’échelle la plus grossière, puis intégrés en tant que données de conditionnement pour générer une nouvelle simulation MPS multi-résolutions. Les résultats obtenus sur le problème synthétique montrent que la méthode converge vers un ensemble de réalisations catégoriques finales cohérent avec l’ensemble catégorique initial. La convergence est fiable en ce sens qu’elle est contrôlée entièrement par l’intégration de la correction de ES-MDA dans les nouvelles simulations MPS multi-résolutions conditionnelles. De plus, grâce à la paramétrisation proposée, l’identification des structures géologiques durant l’assimilation des données est particulièrement efficace pour cet exemple. La comparaison entre l’incertitude estimée et une estimation de référence obtenue avec une méthode de Monte-Carlo révèle que l’incertitude n’est pas sévèrement réduite durant l’assimilation comme cela est souvent observé. La connectivité des structures est bien reproduite durant la procédure itérative malgré la distance plutôt élevée entre les points d’observation., Data assimilation (DA) consists in combining observations and predictions of a numerical model to produce an optimal estimate of the evolving state of a system. Over the last decade, DA methods based on the Ensemble Kalman Filter (EnKF) have been particularly explored in various geoscience fields for inverse modelling. Although this type of ensemble methods can handle high-dimensional systems, they assume that the errors coming from whether the observations or the numerical model are multi-Gaussian. To handle potential nonlinearities between the observations and the state or parameter variables to estimate, iterative variants have been proposed. In this thesis, we first focus on two main iterative ensemble smoother methods for the calibration of a synthetic 2D groundwater model. Using the same set of sparse and transient flow data, we analyse each method when employing them to condition an ensemble of multi-Gaussian hydraulic conductivity fields. We then further explore the application of one iterative ensemble smoother algorithm (ES-MDA) in situations of variable complexity, depending on the geostatistical simulation method used to simulate the prior geological information. The applicability of a parameterization based on the normal-score transform is first investigated. The robustness of the method against nonlinearities is then further explored in the case of discrete facies realizations obtained with a truncated Gaussian technique and updated via their underlying continuous variables. Based on the observed limitations and benefits of the forementioned parameterizations, we finally propose a new methodology for the conditioning of categorical multiple-point statistics (MPS) simulations to dynamic data with a state-of-the-art ensemble Kalman method by taking the example of the Ensemble Smoother with Multiple Data Assimilation (ES-MDA). Our methodology relies on a novel multi-resolution parameterization of the categorical MPS simulation. The ensemble of latent parameters is initially defined on the basis of the coarsest-resolution simulations of an ensemble of multi-resolution MPS simulations. Because this ensemble is non-multi-Gaussian, additional steps prior to the computation of the first update are proposed. In particular, the parameters are updated at predefined locations at the coarsest scale and integrated as hard data to generate a new multi-resolution MPS simulation. The results on the synthetic problem illustrate that the method converges towards a set of final categorical realizations that are consistent with the initial categorical ensemble. The convergence is reliable in the sense that it is fully controlled by the integration of the ES-MDA update into the new conditional multi-resolution MPS simulations. Moreover, thanks to the proposed parameterization, the identification of the geological structures during the data assimilation is particularly efficient for this example. The comparison between the estimated uncertainty and a reference estimate obtained with a Monte Carlo method shows that the uncertainty is not severely reduced during the assimilation as is often the case. The connectivity is successfully reproduced during the iterative procedure despite the rather large distance between the observation points.