Neural solution of elliptic partial differential equation problem for single phase flow in porous media

Partial differential equations are used to model fluid flow in porous media. Neural networks can act as equation solution approximators by basing their forecasts on training samples of permeability maps and their corresponding two-point flux approximation solutions. This paper illustrates how convolutional neural networks of various architecture, depth and parameter configurations manage to forecast solutions of the Darcy’s flow equation for various domain sizes.