Prediction of numerical homogenization using deep learning for the Richards equation

For the nonlinear Richards equation as an unsaturated flow through heterogeneous media, we build a new coarse-scale approximation algorithm utilizing numerical homogenization. This approach follows deep neural networks (DNNs) to quickly and frequently calculate macroscopic parameters. More specifically, train with training set consisting of stochastic permeability realizations corresponding computed targets (effective tensor, homogenized stiffness matrix, right-hand side vector). Our proposed learning scheme develops maps between such fields characteristics, treatment for equation’s nonlinearity is included in predicted which novelty. strategy’s good performance demonstrated by several tests two-dimensional model problems, predictions properties consequently solutions.