Physics-informed neural networks for large deflection analysis of slender piles incorporating non-differentiable soil-structure interaction

Physics-informed neural networks (PINN) is an emerging machine learning technique and has been applied in different areas successfully. To benefit pile analysis from this innovative technique, this paper addresses several problems that arise when extending PINN to the large deflection analysis of slender piles accounting for nonlinear Soil-Structure Interaction (SSI). The governing equations for the structural behavior of piles, considering geometric nonlinearity, are elaborated at first, based on which a PINN framework is constructed correspondingly with a model training process. A series of normalization factors are introduced to the loss function to enhance model training stability. Additionally, a regression-based soil resistance estimation is developed to prevent non-convergence and instability that may occur during the model training when encountering non-differentiable SSI. Extensive examples are provided to validate the robustness and accuracy of the proposed analysis method for piles under complex geological conditions. Furthermore, several case studies are conducted, revealing the necessity of appropriate loss normalization and the effectiveness of regression-based estimation for reflecting non-differentiable functions in the PINN study.