Quantification of Neural Network Uncertainties on the Hydrogeological Predictions by Probability Density Functions

International audienceThe risk of drought impacting the drinking water and agricultural production is worrying in the developed countries, especially in a changing climate context. To manage and prevent this phenomenon, real-time monitoring and predictive systems are emerging as the key solutions. In the field of artificial intelligence, neural networks are one of these predictive systems. This family of parameterized models is a composition of neuronal functions, which apply a non-linear transformation from their inputs to their outputs. These networks are able to learn a hydro(geo)logical system behaviour using a database composed of observed inputs (rainfall, evapotranspiration, etc.) and outputs (groundwater level, discharge, etc.), thanks to an algorithm minimizing a cost function between observed and simulated outputs. However, it remains difficult to assess the uncertainty generated by these models, possibly leading to misinterpretations by the end users. These uncertainties are mainly of three types. The first is related to the input data. Indeed, hydrosystems are surface elements whereas meteorological inputs are punctual elements. The interpolation error can, therefore, be significant because of the lack of knowledge between gauging stations. The second is the neural network model architecture itself. It is possible to deal with this source of uncertainty using regularization methods. Finally, the neural networks are submitted to uncertainties related to parameter initialization, before the training step. The initial parameters may have an important impact on the results. In this paper, we address the prediction of the Blavet groundwater level (Bretagne, France). In order to assess uncertainties, we will first focus on the parameters initialization of the model. Neuronal models are optimized using cross-validation and early stopping. Then, an ensemble model is realized, in which each member is the result of a unique set of parameters initialization. The purpose of the study is to define how many initializations are necessary to obtain a reasonable confidence interval for forecasts, with the smallest interval and the higher rate of observed points inside this interval. The best model will be determined using cross-validation scores thereby ensuring optimal robustness. We show that, in this case study, an ensemble model of 20 different initializations is sufficient to estimate uncertainty while preserving quality. In the second part, the resulting ensemble model will be used to estimate the global model uncertainty using probability density functions (pdf) applied to the distribution of groundwater level data and cross-validation scores of forecasts. It reveals that the groundwater level predictions are composed of two mixed distributions. Therefore, we will use the expectation-maximization algorithm (EM) to obtain parameters of mixed models. Mixed normal and mixed Gumbel laws, among five mixed distributions assessed, give the best groundwater distribution and are able to generate an abacus drawing uncertainty of mode

Spatial analysis of hydraulic conductivity for slope deposits at catchment scale in Northern Tuscany, Italy

Hydraulic conductivity (K) is a relevant engineering geology property of slope deposits (SD) overlying the geological bedrock. This parameter is relevant at the field scale to simulate infiltration and runoff processes, hillslope stability numerical analysis, hydrological studies and environmental issues. Direct measurements (field and laboratory tests), as well as indirect estimations (e:g. correlations from grain size distribution, pedotransfer functions) are available in the literature for estimating K. Many measurements are required to obtain significant results since K depends on many factors such as grain size distribution, bulk density, organic matter, etc. A big set (about 750) of K field measurements in the vadose zone of SD in Northern Tuscany (Italy) has been performed by means of constant and/or falling head permeameter. For each test site (a total of 150 locations), other engineering geology properties of SD such as depth, texture, bulk density, Atterberg limits and grain size distribution have been determined. In this work the local variability of K has been estimated thanks to a statistical analysis of K for each test site. Moreover geostatistical techniques have been applied to infer the spatial correlation of K at the catchment scale. The results show that K varies across the SD profile and in the geographic neighborhood of the test site exhibiting high spatial variability within the study area. The new pedotransfer function, that has been developed with satisfactory results (the determination coefficient R2 = 0.84), suggests that the depth of SD and d20 (is the diameter corresponding to 20% finer in the particle-size distribution) play a relevant role in the prediction of K:These parameters can be considered with profit in spatial analysis of K for SD allowing to produce K maps in the study area

Modélisation par apprentissage statistique des systèmes naturels, ou en interaction avec un environnement naturel. Applications aux karsts, crues éclair et en robotique

This "Habilitation à Diriger les Recherches" report presents a synthesis of research on the modeling of natural systems, or systems in interaction with a natural environment, by machine learning. The specificity of training is first discussed in relation to the calibration and leads to the introduction of the concepts of universal identification and bias-variance dilemma which are then detailed. These concepts are illustrated with regards to the synthesis of a model dedicated to simulation or prediction. Several illustrations are presented such as the training of several behaviors by a mobile robot, the synthesis of a gripper pneumatic controller, and finally the modeling of hydrosystems such as karsts or rapid watersheds. These iconic challenges have in common the availability of databases for several decades, the nonlinearity of the processes involved in these phenomena, the difficulty to measure the state variables, the presence of a considerable noise on the measurements. In order to deal with these difficulties, this report presents how the regularization techniques were reviewed and proposes an original method of semi-physical modeling, the transparent boxes, which allows the physical validation of the model and the deepening of the knowledge one gets about the studied phenomena.Ce mémoire d'Habilitation à Diriger les Recherches présente de manière synthétique les recherches effectuées sur la modélisation par apprentissage statistique de systèmes naturels ou en interaction avec un environnement naturel. La spécificité de l'apprentissage est tout d'abord discutée en relation avec le calage et permet d'introduire les notions d'identification universelle et de dilemme biais-variance qui sont ensuite approfondies dans le mémoire. Ces notions sont illustrées en relation avec la problématique de la synthèse d'un modèle de simulation ou de prédiction. Plusieurs illustrations sont présentées comme l'apprentissage de comportement d'un robot hexapode, la synthèse du contrôleur d'un préhenseur pneumatique et la modélisation d'hydrosystèmes tels les karsts ou les bassins versants rapides. Ces derniers, emblématiques des défis que la science doit permettre d'aborder, ont en commun la disponibilité de bases de données observées depuis plusieurs décennies, la non-linéarité des processus impliqués dans ces phénomènes, la difficulté à mesurer les variables d'état et la présence d'un bruit de mesure considérable. Face à ces difficultés, ce mémoire présente comment les méthodes de régularisation ont été revisitées et propose une démarche originale de modélisation semi physique, les boîtes transparentes, qui permet de valider physiquement le modèle tout en approfondissant la connaissance des phénomènes étudiés

Monitoring of Mescla karst spring French Southern Alps : a rare case of stratified waters out of coastal areas

International audienc

Monitoring of Mescla karst spring in the French Southern Alps. A rare case of stratified waters out of coastal areas

International audienc

Modélisation d'un système karstique par réseaux de neurones : simulation des débits du karst du Baget, France

After a presentation of the karstic systems modelling with neural networks, the paper is devoted to the identification of the rainfall-runoff relation of the Baget karstic system (Ariège-France) with neural networks. First, the flow simulation upon a complete year allows to illustrate the interest of the state feedback operated by neural network. In a second time, the specialisation of the neural network in the "flood" state is implemented in presenting only "flood" periods to the network. It is then satisfying to note that the performance brings results closer to those observed with a state-feedback. Flood simulation allows also to check that, the recurrent directed network having inputs containing more precise information than the static network, the complexity of the architecture may be simplified. In both cases the Nash criteria reach acceptable values between 0.6 and 0.9, which indicate that the quality of the simulation is satisfying, even if climatological data are lacking, except of course rainfall.Après une présentation de la difficulté de la modélisation des systèmes karstiques et de l'identification des systèmes avec des réseaux de neurones formels, cet article se propose d'appliquer les réseaux de neurones pour identifier la relation pluie-débit du système karstique du Baget (Ariège -France). La simulation effectuée sur une année entière permet d'illustrer l 'intérêt du retour d'état que peut apporter le réseau de neurones. Dans un deuxième temps, il est proposé de spécialiser le réseau en mode «crue» en ne lui faisant apprendre, et simuler, que les événements de crue. Il est alors satisfaisant de noter que les performances se rapprochent de celles obtenues avec un retour d 'état. La simulation des crues permet également de vérifier que le réseau récurrent dirigé, possédant des entrées plus riches en information, se satisfait alors d'une architecture simplifiée. Dans tous les cas, les simulations effectuées sont de qualité satisfaisante, conduisant, en l 'absence de données climatiques supplémentaires aux précipitations, à des critères de Nash variant entre 0.6 et 0.9.Johannet Anne, Mangin Alain, Vayssade Bernard. Modélisation d'un système karstique par réseaux de neurones : simulation des débits du karst du Baget, France. In: Collection EDYTEM. Cahiers de géographie, numéro 7, 2008. Karsts de montagne, géomorphologie, patrimoine et ressources. pp. 51-62

Modélisation des hydrosystèmes complexes par machine learning : illustrations sur la prévision des extrêmes hydrologiques (crues, étiages)

National audienc

Conception de modèles de prévision des crues éclair par apprentissage artificiel

PARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF

Taking profit of statistical modelling by neural networks: how to deal with vigilance levels prediction for flash flooding. Case study on Lez Basin (South eastern France).

International audienc

Neural networks-based operational prototype for flash flood forecasting: application to Liane flash floods (France)

The Liane River is a small costal river, famous for its floods, which can affect the city of Boulogne-sur-Mer. Due to the complexity of land cover and hydrologic processes, a black-box non-linear modelling was chosen using neural networks. The multilayer perceptron model, known for its property of universal approximation is thus chosen. Four models were designed, each one for one forecasting horizon using rainfall forecasts: 24h, 12h, 6h, 3h. The desired output of the model is original: it represents the maximal value of the water level respectively 24h, 12h, 6h, 3h ahead. Working with best forecasts of rain (the observed ones during the event in the past), on the major flood of the database in test set, the model provides excellent forecasts. Nash criteria calculated for the four lead times are 0.98 (3h), 0.97 (6h), 0.91 (12h), 0.89 (24h). Designed models were thus estimated as efficient enough to be implemented in a specific tool devoted to real time operational use. The software tool is described hereafter: designed in Java, it presents a friendly interface allowing applying various scenarios of future rainfalls, and a graphical visualization of the predicted maximum water levels and their associated real time observed values