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12 pages, 2843 KiB

Open AccessArticle

Applying Monte Carlo Dropout to Quantify the Uncertainty of Skip Connection-Based Convolutional Neural Networks Optimized by Big Data

by Abouzar Choubineh, Jie Chen, Frans Coenen and Fei Ma

Electronics 2023, 12(6), 1453; https://doi.org/10.3390/electronics12061453 - 19 Mar 2023

Cited by 11 | Viewed by 6993

Abstract

Although Deep Learning (DL) models have been introduced in various fields as effective prediction tools, they often do not care about uncertainty. This can be a barrier to their adoption in real-world applications. The current paper aims to apply and evaluate Monte Carlo (MC) dropout, a computationally efficient approach, to investigate the reliability of several skip connection-based Convolutional Neural Network (CNN) models while keeping their high accuracy. To do so, a high-dimensional regression problem is considered in the context of subterranean fluid flow modeling using 376,250 generated samples. The results demonstrate the effectiveness of MC dropout in terms of reliability with a Standard Deviation (SD) of 0.012–0.174, and of accuracy with a coefficient of determination (R²) of 0.7881–0.9584 and Mean Squared Error (MSE) of 0.0113–0.0508, respectively. The findings of this study may contribute to the distribution of pressure in the development of oil/gas fields. Full article

(This article belongs to the Special Issue Advances of Artificial Intelligence and Vision Applications)

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15 pages, 2568 KiB

Open AccessArticle

Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains

by Valentin Alekseev, Qili Tang, Maria Vasilyeva, Eric T. Chung and Yalchin Efendiev

Computation 2020, 8(2), 58; https://doi.org/10.3390/computation8020058 - 23 Jun 2020

Cited by 5 | Viewed by 3399

Abstract

In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional approximation. For the solution on the fine grid, we construct approximation using the mixed finite element method. To reduce the size of the fine grid system, we will develop a Mixed Generalized Multiscale Finite Element Method (Mixed GMsFEM). The method differs from existing approaches and requires some modifications to represent the flow and magnetic fields. Numerical results are presented for a two-dimensional model problem in perforated domains. This model problem is a special case for the general 3D problem. We study the influence of the number of multiscale basis functions on the accuracy of the method and show that the proposed method provides a good accuracy with few basis functions. Full article

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13 pages, 3157 KiB

Open AccessArticle

Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model

by Denis Spiridonov, Jian Huang, Maria Vasilyeva, Yunqing Huang and Eric T. Chung

Mathematics 2019, 7(12), 1212; https://doi.org/10.3390/math7121212 - 10 Dec 2019

Cited by 10 | Viewed by 3058

Abstract

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. Full article

(This article belongs to the Special Issue Computational Mathematics, Algorithms, and Data Processing)

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17 pages, 347 KiB

Open AccessArticle

Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method

by Eric T. Chung, Yalchin Efendiev, Wing Tat Leung and Jun Ren

Computation 2015, 3(4), 670-686; https://doi.org/10.3390/computation3040670 - 11 Dec 2015

Cited by 5 | Viewed by 5685

Abstract

In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation. We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system. We use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation. We present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation. Full article

(This article belongs to the Special Issue Advances in Modeling Flow and Transport in Porous Media)

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