scholarly journals Prediction of Discretization of GMsFEM Using Deep Learning

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 412 ◽  
Author(s):  
Min Wang ◽  
Siu Wun Cheung ◽  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
Wing Tat Leung ◽  
...  
Keyword(s):  
Neural Networks ◽  
Porous Media ◽  
Deep Learning ◽  
Multiscale Model ◽  
Porous Media Flow ◽  
Scale Parameters ◽  
Flow Problems ◽  
Local Problems ◽  
Nonlinear Relation ◽  
Model Reduction Technique

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. The generalized multiscale finite element method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high-contrast porous media. The key ingredients of GMsFEM include mutlsicale basis functions and coarse-scale parameters, which are obtained from solving local problems in each coarse neighborhood. Given a fixed medium, these quantities are precomputed by solving local problems in an offline stage, and result in a reduced-order model. However, these quantities have to be re-computed in case of varying media (various permeability fields). The objective of our work is to use deep learning techniques to mimic the nonlinear relation between the permeability field and the GMsFEM discretizations, and use neural networks to perform fast computation of GMsFEM ingredients repeatedly for a class of media. We provide numerical experiments to investigate the predictive power of neural networks and the usefulness of the resultant multiscale model in solving channelized porous media flow problems.

scholarly journals Predicting porosity, permeability, and tortuosity of porous media from images by deep learning

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Krzysztof M. Graczyk ◽  
Maciej Matyka
Keyword(s):  
Neural Networks ◽  
Porous Medium ◽  
Porous Media ◽  
Deep Learning ◽  
Lattice Boltzmann ◽  
Good Accuracy ◽  
Two Dimensional ◽  
Empirical Estimate ◽  
Flow Through ◽  
Boltzmann Method

AbstractConvolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($$\varphi$$ φ ), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with $$\varphi \in (0.37,0.99)$$ φ ∈ ( 0.37 , 0.99 ) which covers five orders of magnitude a span for permeability $$k \in (0.78, 2.1\times 10^5)$$ k ∈ ( 0.78 , 2.1 × 10 5 ) and tortuosity $$T \in (1.03,2.74)$$ T ∈ ( 1.03 , 2.74 ) . It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and $$\varphi$$ φ has been obtained and compared with the empirical estimate.

scholarly journals Fronts in two‐phase porous media flow problems: The effects of hysteresis and dynamic capillarity

2020 ◽  
Vol 144 (4) ◽  
pp. 449-492
Author(s):  
K. Mitra ◽  
T. Köppl ◽  
I. S. Pop ◽  
C. J. van Duijn ◽  
R. Helmig
Keyword(s):  
Porous Media ◽  
Porous Media Flow ◽  
Two Phase ◽  
Flow Problems ◽  
Dynamic Capillarity

scholarly journals Physics-Based Deep Learning for Flow Problems

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7760
Author(s):  
Yubiao Sun ◽  
Qiankun Sun ◽  
Kan Qin
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Deep Learning ◽  
Boundary Conditions ◽  
Differential Operators ◽  
Computational Cost ◽  
Initial Boundary ◽  
Machine Learning Algorithms ◽  
Flow Problems ◽  
Target Values

It is the tradition for the fluid community to study fluid dynamics problems via numerical simulations such as finite-element, finite-difference and finite-volume methods. These approaches use various mesh techniques to discretize a complicated geometry and eventually convert governing equations into finite-dimensional algebraic systems. To date, many attempts have been made by exploiting machine learning to solve flow problems. However, conventional data-driven machine learning algorithms require heavy inputs of large labeled data, which is computationally expensive for complex and multi-physics problems. In this paper, we proposed a data-free, physics-driven deep learning approach to solve various low-speed flow problems and demonstrated its robustness in generating reliable solutions. Instead of feeding neural networks large labeled data, we exploited the known physical laws and incorporated this physics into a neural network to relax the strict requirement of big data and improve prediction accuracy. The employed physics-informed neural networks (PINNs) provide a feasible and cheap alternative to approximate the solution of differential equations with specified initial and boundary conditions. Approximate solutions of physical equations can be obtained via the minimization of the customized objective function, which consists of residuals satisfying differential operators, the initial/boundary conditions as well as the mean-squared errors between predictions and target values. This new approach is data efficient and can greatly lower the computational cost for large and complex geometries. The capacity and generality of the proposed method have been assessed by solving various flow and transport problems, including the flow past cylinder, linear Poisson, heat conduction and the Taylor–Green vortex problem.

scholarly journals An OpenMP implementation of the MuMM solver for porous media flow problems

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
Sérgio Felipe Ferreira Silva ◽  
Hanna Thaina Prates Arimatéia ◽  
Alexandre Santos Francisco ◽  
Weslley Luiz da Silva Assis
Keyword(s):  
Porous Media ◽  
Domain Decomposition ◽  
Iterative Procedure ◽  
Application Programming Interface ◽  
Heterogeneous Porous Media ◽  
Computational Effort ◽  
Multiscale Methods ◽  
Porous Media Flow ◽  
Flow Problems ◽  
Second Order Elliptic Problems

Multiscale methods are usually developed for solving second-order elliptic problems in which coefficients are of multiscale heterogeneous nature. The Multiscale Mixed Method (MuMM) was introduced aiming at the efficient and accurate approximation of large flow problems in highly heterogeneous porous media. In the MuMM numerical solver, first mixed multiscale basis functions are constructed, and next global domain decomposition iterations are performed to compute the discrete solution of the problems. However, this iterative procedure is a time-consuming step. In this paper, the authors improve the MuMM solver through the implementation of parallel computations in the step concerning the global iterative procedure. The parallel version of the solver employs the application programming interface Open Multi-Processing (OpenMP). The implementation with the OpenMP reduces significantly the computational effort to perform the domain decomposition iterations, as indicated by the numerical results.

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