Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media

Vasilyeva, Maria; Tyrylgin, Aleksei

doi:10.48550/arxiv.1810.01586

Cited by 5 publications

(5 citation statements)

References 21 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where N H is the number of the coarse grid cells, K i is the quadrilateral coarse cell and i is the coarse grid cell index [37,31]. Form of the coarse grid upscaled model is similar to the fine grid model with finite volume approximation, where coarse grid transmissibilities T U P ij are calculated by a solution of the local problems that take into account fine grid resolution of the heterogeneous permeability (see Figure 1).…”

Section: Coarse Grid Upscaled Modelmentioning

confidence: 99%

“…Local model reduction techniques are based on constructing local multiscale basis functions to represent the influence of small scale heterogeneity [30,4,34,35]. One of the widely used ways is based on the numerical homogenization technique, where effective parameters are calculated in order to construct coarse grid approximations [2,29,37]. The coarse grid parameters are constructed by solving local problems with appropriate boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques

Vasilyeva

Leung

Chung

et al. 2020

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are formulated as general multicontinuum models. We construct a fine grid approximation using the finite volume method and embedded discrete fracture model. Macroscopic models for these complex nonlinear systems require nonlocal multicontinua approaches, which are developed in earlier works [8]. These rigorous techniques require complex local computations, which involve solving local problems in oversampled regions subject to constraints. The solutions of these local problems can be replaced by solving original problem on a coarse (oversampled) region for many input parameters (boundary and source terms) and computing effective properties derived by nonlinear nonlocal multicontinua approaches. The effective properties depend on many variables (oversampled region and the number of continua), thus their calculations require some type of machine learning techniques. In this paper, our contribution is two fold. First, we present macroscopic models and discuss how to effectively compute macroscopic parameters using deep learning algorithms. The proposed method can be regarded as local machine learning and complements our earlier approaches on global machine learning [39,38]. We consider a coarse grid approximation using two upscaling techniques with single phase upscaled transmissibilities and nonlocal nonlinear upscaled transmissibilities using a machine learning algorithm. We present results for two model problems in heterogeneous and fractured porous media and show that the presented method is highly accurate and provides fast coarse grid calculations.

show abstract

Section: Coarse Grid Upscaled Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques

Vasilyeva

Leung

Chung

et al. 2020

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…deep-trained FE [49], that aim to resolve computational bottlenecks in FE. Furthermore, neural networks have demonstrated unprecedented efficiency in predicting the solutions of computationally expensive simulations, such as nonlinear finite element analysis [50,51], convective operation [52], asymptotic homogenization [53,54], and multiscale analysis [55].…”

Section: Introductionmentioning

confidence: 99%

An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting

Lee

Kang²,

Jung

et al. 2023

Engineering with Computers

View full text Add to dashboard Cite

Enrichment techniques that employ nonconforming mesh are effective in modeling structures with discontinuities because numerical issues regarding mesh quality are avoided. However, the accurate integration of the bilinear and linear forms on the discretized domain, which is required in the standard Galerkin-based finite element method, is computationally expensive due to the complexity of the enriched basis function. In this paper, we present a fast and accurate alternative method of numerical integration using nonlinear regression enabled by a multiperceptron feedforward neural network. The relationship between an implicitly represented geometry and the quadrature rule derived from the moment fitting method is predicted by the neural network; the neural network-based regression model circumvents complex computation and significantly reduces the overall online time by avoiding expensive function evaluations. Through the selected numerical examples, we demonstrate the efficiency and accuracy of the current method, as well as the flexibility of the trained network to be used in different contexts.

show abstract

“…Within recent years, numerous efforts have been made to apply this promising technique to related researches in oil and gas industry. A deep neural network is constructed in [24] to learn a map between stochastic fields and effective properties for fast calculation of the effective properties in subsurface reservoirs for a coarse grid approximation of the problem and a more remarkable progress is reported in [25] using Convolutional neural network (CNN) for high-dimensional problems. A regression model is developed in [26] to predict the equilibrium coefficients using ANN, and both relevance vector machines (RVM) and ANN are applied in [27] to reduce the cost of phase-equilibrium calculations for compositional models.…”

Section: Introductionmentioning

confidence: 99%

A self-adaptive deep learning algorithm for accelerating multi-component flash calculation

Tao

Liu

et al. 2020

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media

Cited by 5 publications

References 21 publications

Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques

Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques

An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting

A self-adaptive deep learning algorithm for accelerating multi-component flash calculation

Contact Info

Product

Resources

About