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.

Keywords

• subsurface fluid flow
• Fourier neural operator
• small-shape data
• finite element method
• convolutional neural network
• sensitivity analysis