Physics informed deep learning for coupled flow and poromechanics. Mandel’s problem

Abstract

We evaluate the performance of the physics informed deep learning paradigm for solving the Biot system modeling coupled flow and poromechanics using Mandel’s problem analytical solution. The solution presents a unique set of challenges to the deep learning paradigm, such as the disparity in expected orders of magnitude of the output variables as well as the non-monotonicity and steep gradient in one of the output variables in a certain spatio-temporal domain. We tackle those challenges in this work and comment on the effect of activation function and minimization algorithm on the deep learning framework.