Preconditioning Markov Chain Monte Carlo Method for Geomechanical Subsidence using multiscale method and machine learning technique

Vasilyeva, Maria; Tyrylgin, Aleksei; Brown, Donald L.; Mondal, Anirban

doi:10.1016/j.cam.2021.113420

Cited by 20 publications

(9 citation statements)

References 30 publications

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“…By using this combination, the search found papers that study the training of neural networks to perform inverse analysis, [39][40][41] which uses in loco measurements to build meta models for the massive. [42][43][44][45][46][47][48] In these works, neural networks are used to build constitutive models based on laboratory tests. 49,50 Only one research work was found that proposes a numerical method based on machine learning.…”

Section: Systematic Literature Reviewmentioning

confidence: 99%

“…No exclusions were made based on the year of publication. By using this combination, the search found papers that study the training of neural networks to perform inverse analysis, 39–41 which uses in loco measurements to build meta models for the massive 42–48 . In these works, neural networks are used to build constitutive models based on laboratory tests 49,50 .…”

Section: Systematic Literature Reviewmentioning

confidence: 99%

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Intelligent element: Coupling Green function approach and artificial intelligence to reduce discretization effort

Peres

Sotelino

Mesquita

2023

Num Anal Meth Geomechanics

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This research work presents a method that modifies a classical numerical method using artificial intelligence (AI) and takes advantage of an analytical method to minimize the usual need for increasing discretization. Its formulation is based on the integration of two main concepts: the reciprocity theorem and the generalization capability of artificial neural networks (ANNs). The reciprocity theorem is used to formulate the mathematical expression governing the geomechanical problem, which is then discretized in space into intelligent elements. The behavior of the strain field inside these new elements is predicted using an ANN. To make these predictions, the neural network uses displacement boundary conditions, material properties, and the geometric shape of the element as input data. The comparison was performed for two examples, in which the first had a uniform depletion of the reservoir, while the second had a non-uniform variation of the pore pressure. For the same level of accuracy, the proposed method was 10 times faster than the traditional method for the first example and five times faster for the second example on a computer with 12 threads of 2.6 GHz and 32 GB RAM.

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Section: Systematic Literature Reviewmentioning

confidence: 99%

Section: Systematic Literature Reviewmentioning

confidence: 99%

Intelligent element: Coupling Green function approach and artificial intelligence to reduce discretization effort

Peres

Sotelino

Mesquita

2023

Num Anal Meth Geomechanics

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“…Afterward, we assume that the multiscale high-contrast coefficient κ(x) = κ(x, ω) in Eq. (2.3) is stochastic [60]. However, the stochastic symbol ω is eliminated for the sake of simplicity.…”

Section: Model Problemmentioning

confidence: 99%

“…Our goal in this study is to use deep neural networks (DNNs) to simulate the connection between the online GMsFEM's main component, namely online multiscale basis functions, and the heterogeneous permeability coefficients κ(x) (so the hydraulic conductivity coefficients κ(x, p(t, x))). It should be noted that the Karhunen-Loève expansion (KLE) [56,60] is used to create our random heterogeneous permeability fields. After this relationship is established, we can supply the network with any realization of the permeability field (so the conductivity field with the provided solution data from the previous Picard iteration) to extract the matching online multiscale basis functions and then restore the fine-scale GMsFEM solution to (2.3).…”

Section: For Implementationmentioning

confidence: 99%

Prediction of numerical homogenization using deep learning for the Richards equation

Stepanov

Spiridonov

Mai

2023

Journal of Computational and Applied Mathematics

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“…In this work, we use an embedded fractured model (EFM) that allows constructing mesh for fracture networks independently of porous media mesh [28][29][30]. However, a detailed fine grid is still required for a heterogeneous porous media with high contrast coefficients [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model

et al. 2019

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In this paper, the solution of the Darcy-Forchheimer model in high contrast heterogeneous media is studied. This problem is solved by a mixed finite element method (MFEM) on a fine grid (the reference solution), where the pressure is approximated by piecewise constant elements; meanwhile, the velocity is discretized by the lowest order Raviart-Thomas elements. The solution on a coarse grid is performed by using the mixed generalized multiscale finite element method (mixed GMsFEM). The nonlinear equation can be solved by the well known Picard iteration. Several numerical experiments are presented in a two-dimensional heterogeneous domain to show the good applicability of the proposed multiscale method.

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Preconditioning Markov Chain Monte Carlo Method for Geomechanical Subsidence using multiscale method and machine learning technique

Cited by 20 publications

References 30 publications

Intelligent element: Coupling Green function approach and artificial intelligence to reduce discretization effort

Intelligent element: Coupling Green function approach and artificial intelligence to reduce discretization effort

Prediction of numerical homogenization using deep learning for the Richards equation

Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model

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