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A physics-informed neural network is presented for poroelastic problems withcoupled flow and deformation processes. The governing equilibrium and massbalance equations are discussed and specific derivations for two-dimensionalcases are presented. A fully-connected deep neural network is used fortraining. Barry and Mercer's source problem with time-dependent fluidinjection/extraction in an idealized poroelastic medium, which has an exactanalytical solution, is used as a numerical example. A random sample from theanalytical solution is used as training data and the performance of the modelis tested by predicting the solution on the entire domain after training. Thedeep learning model predicts the horizontal and vertical deformations wellwhile the error in the predicted pore pressure predictions is slightly higherbecause of the sparsity of the pore pressure values.

Physics-informed deep learning for flow and deformation in poroelastic media