Choubineh, Abouzar
(2023)
Machine Learning-based Generalized Multiscale Finite Element Method and its Application in Reservoir Simulation.
PhD thesis, University of Liverpool.
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Abstract
In multiscale modeling of subsurface fluid flow in heterogeneous porous media, standard polynomial basis functions are replaced by multiscale basis functions, which are used to predict pressure distribution. To produce such functions in the mixed Generalized Multiscale Finite Element Method (GMsFEM), a number of Partial Differential Equations (PDEs) must be solved, leading to significant computational overhead. The main objective of the work presented in this thesis was to investigate the efficiency of Machine Learning (ML)/Deep Learning (DL) models in reconstructing the multiscale basis functions (Basis 2, 3, 4, and 5) of the mixed GMsFEM. To achieve this, four standard models named SkiplessCNN models were first developed to predict four different multiscale basis functions. These predictions were based on two distinct datasets (initial and extended) generated, with the permeability field being the sole input. Subsequently, focusing on the extended dataset, three distinct skip connection schemes (FirstSkip, MidSkip, and DualSkip) were incorporated into the SkiplessCNN architecture. Following this, the four developed models - SkiplessCNN, FirstSkipCNN, MidSkipCNN, and DualSkipCNN - were separately combined using linear regression and ridge regression within the framework of Deep Ensemble Learning (DEL). Furthermore, the reliability of the DualSkipCNN model was examined using Monte Carlo (MC) dropout. Ultimately, two Fourier Neural Operator (FNO) models, operating on infinite-dimensional spaces, were developed based on a new dataset for directly predicting pressure distribution. Based on the results, sufficient data for the validation and testing subsets could help decrease overfitting. Additionally, all three skip connections were found to be effective in enhancing the performance of SkiplessCNN, with DualSkip being the most effective among them. As evaluated on the testing subset, the combined models using linear regression and ridge regression significantly outperformed the individual models for all basis functions. The results also confirmed the robustness of MC dropout for DualSkipCNN in terms of epistemic uncertainty. Regarding the FNO models, it was discovered that the inclusion of a MultiLayer Perceptron (MLP) in the original Fourier layers significantly improved the prediction performance on the testing subset. Looking at this work as an image (matrix)-to-image (matrix) problem, the developed data-driven models through various techniques could find applications beyond reservoir engineering.
| Item Type: | Thesis (PhD) |
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| Uncontrolled Keywords: | subsurface fluid flow, finite element method, applied machine learning/deep learning, big data, reliability, neural operator |
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 01 Feb 2024 16:25 |
| Last Modified: | 01 Feb 2024 16:26 |
| DOI: | 10.17638/03176715 |
| Supervisors: |
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| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3176715 |
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