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

Abstract

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.