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

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