Multiscale model reduction for fluid infiltration simulation through dual-continuum porous media with localized uncertainties

Li, Qiuqi; Wang, Yuhe; Vasilyeva, Maria

doi:10.1016/j.cam.2017.12.040

Cited by 14 publications

(9 citation statements)

References 42 publications

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“…Several lines of research have been pursued to address this challenge. For instance, models of multiple continuum media [15,16,17], dual mesh approaches [18,19,20], upscaling [21,22,23,24] and model reduction [25,26,27,28] techniques have been developed to decrease the run-time of a single simulation. Also, various surrogate modeling techniques [29,30,31] emerged in order to reduce the cost of evaluating a large number of expensive numerical simulations.…”

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confidence: 99%

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Tarakanov¹,

Elsheikh²

2019

Journal of Computational Physics

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Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a data-driven regression-based technique that relies on spectral polynomials as basis-functions. In this technique, the outputs of few numerical simulations are used to estimate the PCE coefficients within a regression framework combined with regularization techniques where the regularization parameters are estimated using standard cross-validation as applied in supervised machine learning methods.In the present work, we introduce an efficient method for estimating the PCE coefficients combining Elastic Net regularization with a data-driven feature ranking approach. Our goal is to increase the probability of identifying the most significant PCE components by assigning each of the PCE coefficients a numerical value reflecting the magnitude of the coefficient and its stability with respect to perturbations in the input data. In our evaluations, the proposed approach has shown high convergence rate for high-dimensional problems, where standard feature ranking might be challenging due to the curse of dimensionality.The presented method is implemented within a standard machine learning library (scikit-learn [1]) allowing for easy experimentation with various solvers and regularization techniques (e.g. Tikhonov, LASSO, LARS, Elastic Net) and enabling automatic cross-validation techniques using a widely used and well tested implementation. We present a set of numerical tests on standard analytical functions, a two-phase subsurface flow model and a simulation dataset for CO2 sequestration in a saline aquifer. For all test cases, the proposed approach resulted in a significant increase in PCE convergence rates.

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confidence: 99%

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Tarakanov¹,

Elsheikh²

2019

Journal of Computational Physics

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“…for some constant D 2 > 0. By spectral problem (17) and the orthogonality of eigenfunctions {ψ ωj k } k , we have…”

Section: A2 Proof Of Theoremmentioning

confidence: 99%

“…And later, a third continua was introduced by researchers to generalize the application of such an idea [20,27,25,24]. Thanks to the simplicity and flexibility of this method, it has been widely adopted in many fields [17]. However, the limitation of the multi-continuum model is also prominent, as it assumes all continuum are connected globally.…”

Section: Introductionmentioning

confidence: 99%

Generalized multiscale multicontinuum model for fractured vuggy carbonate reservoirs

Wang

Cheung

Chung

et al. 2020

Journal of Computational and Applied Mathematics

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Simulating flow in a highly heterogeneous reservoir with multiscale characteristics could be considerably demanding. To tackle this problem, we propose a numerical scheme coupling the Generalized Multiscale Finite Element Method (GMsFEM) with a triple-continuum model aimed at a faster simulator framework that can explicitly represent the interactions among different continua. To further enrich the descriptive ability of our proposed model, we combine the Discrete Fracture Model (DFM) to model the local effects of discrete fractures. In the proposed model, GMsFEM, as an advanced model reduction technique, enables capturing the multiscale flow dynamics. This is accomplished by systematically generating an approximation space through solving a series of local snapshot and spectral problems. The resulting eigen-functions can pass the local features to the global level when acting as basis functions in coarse problems. Our goal in this paper is to further improve the accuracy of flow simulation in complicated reservoirs especially for the case when multiple discrete fractures located in single coarse neighborhood and multiscale finite element methods fail. Together with a detailed description of the model, several numerical experiments are conducted to confirm the success of our proposed method. A rigid proof is also given in the aspect of numerical analysis.

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“…Here, the bk-model is approximated in space using the Finite Element Method (FEM). The POD-greedy procedure has been combined with FEM in previous work [25,18,4].…”

Section: Introductionmentioning

confidence: 99%

Reducing sensors for transient heat transfer problems by means of variational data assimilation

Benaceur¹

2021

The SMAI Journal of Computational Mathematics

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We propose a contribution that combines model reduction with data assimilation. A dedicated Parametrized Background Data-Weak (PBDW) approach has been introduced in the literature so as to combine numerical models with experimental measurements. We extend the approach to a time-dependent framework by means of a POD-greedy reduced basis construction. Since the construction of the basis is performed offline, the algorithm addresses the time dependence of the problem while the time stepping scheme remains unchanged. Moreover, we devise a new algorithm that exploits offline state estimates in order to diminish both the dimension of the online PBDW statement and the number of required sensors collecting data. The idea is to exploit in situ observations in order to update the best-knowledge model, thereby improving the approximation capacity of the background space.

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Multiscale model reduction for fluid infiltration simulation through dual-continuum porous media with localized uncertainties

Cited by 14 publications

References 42 publications

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Generalized multiscale multicontinuum model for fractured vuggy carbonate reservoirs

Reducing sensors for transient heat transfer problems by means of variational data assimilation

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