Data-driven forward and inverse analysis of two-dimensional soil consolidation using physics-informed neural network

Abstract

Employing machine learning algorithms to forecast the behavior of nonlinear spatiotemporal systems, such as soil consolidation induced by land reclamation, has been popular in recent years. Although pure data-driven models demonstrate strong performance within their training domain, i.e., in-sample prediction, they lack interpretability and might have poor generalization outside the training domain, i.e., out-of-sample prediction, particularly when the observed geodata is limited. Moreover, these models often disregard valuable geotechnical domain knowledge. To address these limitations, a novel physics-informed neural network (PINN) is developed for both forward and inverse analyses of two-dimensional soil consolidations when only limited measurements are available. Different random seeds are used to test the robustness of the PINN developed and quantify the associated model uncertainty. Plane strain and axisymmetric consolidation partial differential equations serve as valuable prior domain knowledge to regulate the model training and optimization process in PINN. The performance of PINN is illustrated using both simulated and real consolidation examples. Results indicate that PINN can accurately approximate spatiotemporal pore pressure response and exhibits excellent generalization performance. More importantly, PINN renders an efficient identification of unknown governing parameters from limited measurements with quantified statistical uncertainty, which diminishes as measurement data increase. Furthermore, a real example shows that PINN is capable of discovering the nonlinear decay of horizontal permeability around a prefabricated vertical drain (PVD) based on limited data, tackling the challenge of specifying a smear zone and its permeability distribution in PVD design.