Fourier Neural Operator for Fluid Flow in Small-Shape 2D Simulated Porous Media Dataset

Choubineh, Abouzar, Chen, Jie, Wood, David A, Coenen, Frans ORCID: 0000-0003-1026-6649 and Ma, Fei ORCID: 0000-0001-6099-480X (2023) Fourier Neural Operator for Fluid Flow in Small-Shape 2D Simulated Porous Media Dataset. ALGORITHMS, 16 (1). p. 24.

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Official URL: http://dx.doi.org/10.3390/a16010024

Abstract

<jats:p>Machine Learning (ML) and/or Deep Learning (DL) methods can be used to predict fluid flow in porous media, as a suitable replacement for classical numerical approaches. Such data-driven approaches attempt to learn mappings between finite-dimensional Euclidean spaces. A novel neural framework, named Fourier Neural Operator (FNO), has been recently developed to act on infinite-dimensional spaces. A high proportion of the research available on the FNO has focused on problems with large-shape data. Furthermore, most published studies apply the FNO method to existing datasets. This paper applies and evaluates FNO to predict pressure distribution over a small, specified shape-data problem using 1700 Finite Element Method (FEM) generated samples, from heterogeneous permeability fields as the input. Considering FEM-calculated outputs as the true values, the configured FNO model provides superior prediction performance to that of a Convolutional Neural Network (CNN) in terms of statistical error assessment based on the coefficient of determination (R2) and Mean Squared Error (MSE). Sensitivity analysis considering a range of FNO configurations reveals that the most accurate model is obtained using modes=15 and width=100. Graphically, the FNO model precisely follows the observed trend in each porous medium evaluated. There is potential to further improve the FNO’s performance by including physics constraints in its network configuration.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	subsurface fluid flow, Fourier neural operator, small-shape data, finite element method, convolutional neural network, sensitivity analysis
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	06 Jan 2023 10:49
Last Modified:	21 Feb 2023 10:00
DOI:	10.3390/a16010024
Open Access URL:	https://www.mdpi.com/1999-4893/16/1/24
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3166837