On Physics-Informed Neural Networks training for coupled hydro-poromechanical problems

The robust and efficient numerical solution of coupled hydro-poromechanical problems is of paramount importance in many application fields, in particular in geomechanics and biomechanics. Even though the solution by means of the Finite Elements Method (FEM) still remains the preferred option, Physics-Informed Neural Networks (PINNs) are rapidly gaining attention as a powerful and promising approach. By involving the residual of the governing PDEs as a constraint in the training, PINNs combine a physics-driven approach together with a data-driven one, leveraging on deep learning techniques. This work focuses on coupled hydro-poromechanical processes, where a PINN-based approach is implemented and investigated in classical benchmarks. An analysis of the influence of the hyper-parameter selection has been performed to study the model sensitivity to PINN architecture and identify the most appropriate one. To take advantage of PINN ability to integrate data and reduce the complexity of the solution of the coupled hydro-poromechanical problem, a "sensor-driven" training is proposed where data are provided at locations inside the domain even to solve a forward problem. The goal is to assess and validate the approach, thus contributing to the foundation of this method in coupled hydro-poromechanics.