Modeling One-Dimensional Nonlinear Consolidation Problems by Physics-Informed Neural Network with Layer-Wise Locally Adaptive Activation Functions

The study on soil consolidation and settlement is of great importance in geotechnical engineering practice. Nowadays, physics-informed neural networks (PINN) are becoming more and more popular in solving geotechnical engineering problems thanks to their meshless, physically constrained, and data-driven nature. Although there have been some successful applications in one-dimensional (1D) consolidation problems in saturated soils, the ability and stability to deal with more complex boundary conditions remain to be tested. In this paper, the effects of activation function and random state on the PINN are investigated for solving two 1D consolidation problems in saturated soils, and the proposed method for inverse modeling of the two 1D consolidation problems. The results show that PINN with layer-wise locally adaptive activation functions improves the convergence speed and prediction accuracy of the PINN for solving the 1D nonlinear soil consolidation problems, and at the same time the robustness of the model to random states. Moreover, the proposed method still converges faster in the inverse modeling of 1D consolidation problems.