Uncertainty quantification in coastal aquifers using the multilevel Monte Carlo method

We consider a class of density-driven flow problems. We are particularly interested in the problem of the salinization of coastal aquifers. We consider the Henry saltwater intrusion problem with uncertain porosity, permeability, and recharge parameters as a test case. The reason for the presence of uncertainties is the lack of knowledge, inaccurate measurements, and inability to measure parameters at each spatial or time location. This problem is nonlinear and time-dependent. The solution is the salt mass fraction, which is uncertain and changes in time. Uncertainties in porosity, permeability, recharge, and mass fraction are modeled using random fields. This work investigates the applicability of the well-known multilevel Monte Carlo (MLMC) method for such problems. The MLMC method can reduce the total computational and storage costs. Moreover, the MLMC method runs multiple scenarios on different spatial and time meshes and then estimates the mean value of the mass fraction. The parallelization is performed in both the physical space and stochastic space. To solve every deterministic scenario, we run the parallel multigrid solver ug4 in a black-box fashion. We use the solution obtained from the quasi-Monte Carlo method as a reference solution.Comment: 24 pages, 3 tables, 11 figure

Super learner implementation in corrosion rate prediction

This thesis proposes a new machine learning model for predicting the corrosion rate of 3C steel in seawater. The corrosion rate of a material depends not just on the nature of the material but also on the material\u27s environmental conditions. The proposed machine learning model comes with a selection framework based on the hyperparameter optimization method and a performance evaluation metric to determine the models that qualify for further implementation in the proposed models’ ensembles architecture. The major aim of the selection framework is to select the least number of models that will fit efficiently (while already hyperparameter-optimized) into the architecture of the proposed model. Subsequently, the proposed predictive model is fitted on some portion of a dataset generated from an experiment on corrosion rate in five different seawater conditions. The remaining portion of this dataset is implemented in estimating the corrosion rate. Furthermore, the performance of the proposed models’ predictions was evaluated using three major performance evaluation metrics. These metrics were also used to evaluate the performance of two hyperparameter-optimized models (Smart Firefly Algorithm and Least Squares Support Vector Regression (SFA-LSSVR) and Support Vector Regression integrating Leave Out One Cross-Validation (SVR-LOOCV)) to facilitate their comparison with the proposed predictive model and its constituent models. The test results show that the proposed model performs slightly below the SFA-LSSVR model and above the SVR-LOOCV model by an RMSE score difference of 0.305 and RMSE score of 0.792. Despite its poor performance against the SFA-LSSVR model, the super learner model outperforms both hyperparameter-optimized models in the utilization of memory and computation time (graphically presented in this thesis)

Das unstetige Galerkinverfahren für Strömungen mit freier Oberfläche und im Grundwasserbereich in geophysikalischen Anwendungen

Free surface flows and subsurface flows appear in a broad range of geophysical applications and in many environmental settings situations arise which even require the coupling of free surface and subsurface flows. Many of these application scenarios are characterized by large domain sizes and long simulation times. Hence, they need considerable amounts of computational work to achieve accurate solutions and the use of efficient algorithms and high performance computing resources to obtain results within a reasonable time frame is mandatory. Discontinuous Galerkin methods are a class of numerical methods for solving differential equations that share characteristics with methods from the finite volume and finite element frameworks. They feature high approximation orders, offer a large degree of flexibility, and are well-suited for parallel computing. This thesis consists of eight articles and an extended summary that describe the application of discontinuous Galerkin methods to mathematical models including free surface and subsurface flow scenarios with a strong focus on computational aspects. It covers discretization and implementation aspects, the parallelization of the method, and discrete stability analysis of the coupled model.Für viele geophysikalische Anwendungen spielen Strömungen mit freier Oberfläche und im Grundwasserbereich oder sogar die Kopplung dieser beiden eine zentrale Rolle. Oftmals charakteristisch für diese Anwendungsszenarien sind große Rechengebiete und lange Simulationszeiten. Folglich ist das Berechnen akkurater Lösungen mit beträchtlichem Rechenaufwand verbunden und der Einsatz effizienter Lösungsverfahren sowie von Techniken des Hochleistungsrechnens obligatorisch, um Ergebnisse innerhalb eines annehmbaren Zeitrahmens zu erhalten. Unstetige Galerkinverfahren stellen eine Gruppe numerischer Verfahren zum Lösen von Differentialgleichungen dar, und kombinieren Eigenschaften von Methoden der Finiten Volumen- und Finiten Elementeverfahren. Sie ermöglichen hohe Approximationsordnungen, bieten einen hohen Grad an Flexibilität und sind für paralleles Rechnen gut geeignet. Diese Dissertation besteht aus acht Artikeln und einer erweiterten Zusammenfassung, in diesen die Anwendung unstetiger Galerkinverfahren auf mathematische Modelle inklusive solcher für Strömungen mit freier Oberfläche und im Grundwasserbereich beschrieben wird. Die behandelten Themen umfassen Diskretisierungs- und Implementierungsaspekte, die Parallelisierung der Methode sowie eine diskrete Stabilitätsanalyse des gekoppelten Modells

Dynamics of coastal aquifers: data-driven forecasting and risk analysis

This work is focused on the study of saltwater intrusion in coastal aquifers, and in particular on the realization of conceptual schemes to evaluate the risk associated with it. Saltwater intrusion depends on different natural and anthropic factors, both presenting a strong aleatory behaviour, that should be considered for an optimal management of the territory and water resources. Given the uncertainty of problem parameters, the risk associated with salinization needs to be cast in a probabilistic framework. On the basis of a widely adopted sharp interface formulation, key hydrogeological problem parameters are modeled as random variables, and global sensitivity analysis is used to determine their influence on the position of saltwater interface. The analyses presented in this work rely on an efficient model reduction technique, based on Polynomial Chaos Expansion, able to combine the best description of the model without great computational burden. When the assumptions of classical analytical models are not respected, and this occurs several times in the applications to real cases of study, as in the area analyzed in the present work, one can adopt data-driven techniques, based on the analysis of the data characterizing the system under study. It follows that a model can be defined on the basis of connections between the system state variables, with only a limited number of assumptions about the "physical" behaviour of the system

Measurements, Models, Systems and Design

531 s.

Synthetic modelling study of marine controlled-source electromagnetic data for hydrocarbon exploration

The marine controlled-source electromagnetic method (CSEM) is a geophysical technique for mapping subsurface electrical resistivity structure in the offshore environment. It has gained ground in recent years as a tool for remote detection and mapping of hydrocarbon reservoirs as it serves as an independent yet complementary method to seismic acquisition. While CSEM data contains useful information about the subsurface, modelling and inversion are required to convert data into interpretable resistivity images. Improvement of modelling tools will assist in closing the gap between acquisition and interpretation of CSEM data. The primary focus of this study was to explore the limits of our present modelling capabilities in the context of marine electromagnetic scenarios. Software based on the three-dimensional CSEM finite-element forward code CSEM3DFWD (Ansari and Farquharson, 2014; Ansari et al., 2015) was employed in this study. While testing of this software had been expanded to models of relevance to mineral exploration, its performance for models which are representative of marine geologic environments, in particular those which are encountered in offshore oil and gas exploration, had not yet been investigated. In this study, marine models of increasing complexity were built and tested, with the ultimate goal of synthesizing marine CSEM data for three-dimensional earth models which were complete in their description of the subsurface. Computed responses were compared to results existing in the literature, when available. To investigate the capability of the code in modelling realistic scenarios, forward solutions were computed for a marine reservoir model based on the real-life North Amethyst oil field, located in the Jeanne d’Arc Basin, offshore Newfoundland. When the capability of modelling realistic earth models is fully realized, forward modelling may be used to assess the utility of the marine CSEM method as a tool for hydrocarbon detection and delineation in specific offshore scenarios

2nd International Conference on Numerical and Symbolic Computation

The Organizing Committee of SYMCOMP2015 – 2nd International Conference on Numerical and Symbolic Computation: Developments and Applications welcomes all the participants and acknowledge the contribution of the authors to the success of this event. This Second International Conference on Numerical and Symbolic Computation, is promoted by APMTAC - Associação Portuguesa de Mecânica Teórica, Aplicada e Computacional and it was organized in the context of IDMEC/IST - Instituto de Engenharia Mecânica. With this ECCOMAS Thematic Conference it is intended to bring together academic and scientific communities that are involved with Numerical and Symbolic Computation in the most various scientific area