Physics-informed Neural Networks for Heterogeneous Poroelastic Media

This study introduces a novel physics-informed neural networks (PINNs) framework designed to model coupled-field problems specifically tailored for heterogeneous poroelastic media. Firstly, a composite neural network is developed where distinct neural networks are dedicated to predicting displacement and pressure variables for each material, employing identical activation functions but trained separately across all other parameters. Secondly, we handle the challenges of heterogeneous material interfaces by the Interface- PINNs (I-PINNs) framework, where different activation functions across any material interface are prescribed to ensure that the discontinuities in solution fields and gradients are accurately captured. We compare the modified PINNs framework with the conventional approach on two one-dimensional benchmark examples for poroelasticity in heterogeneous media. Furthermore, we assess a single neural network architecture, comparing it against the composite neural network proposed in this work. These examples show that the proposed framework demonstrates superior approximation accuracy in both displacements and pressures, and better convergence behavior.