Physics-informed neural networks with curriculum training for poroelastic flow and deformation processes

Physics-Informed Neural Networks (PINNs) have emerged as a highly active research topic across multiple disciplines in science and engineering, including computational geomechanics. PINNs offer a promising approach in different applications where faster, near real-time or real-time numerical prediction is required. Examples of such areas in geomechanics include geotechnical design optimization, digital twins of geo-structures and stability prediction of monitored slopes. But there remain challenges in training of PINNs, especially for problems with high spatial and temporal complexity. In this paper, we study how the training of PINNs can be improved by using an idealized poroelasticity problem as a demonstration example. A curriculum training strategy is employed where the PINN model is trained gradually by dividing the training data into intervals along the temporal dimension. We find that the PINN model with curriculum training takes nearly half the time required for training compared to conventional training over the whole solution domain. For the particular example here, the quality of the predicted solution was found to be good in both training approaches, but it is anticipated that the curriculum training approach has the potential to offer a better prediction capability for more complex problems, a subject for further research.