Novel integration of FEM, Physics-Informed Neural Networks, and explainable Metaheuristics for retaining wall analysis

<p dir="ltr">This study presents an integrated approach for predicting the Factor of Safety (FOS) of cantilever retaining walls by combining Finite Element Method (FEM)-based simulations with a hybrid Physics-Informed Neural Network (PINN) and Explainable Metaheuristic-Optimized Extreme Gradient Boosting (XGBoost) model. A comprehensive dataset comprising 108 simulation scenarios was generated using GeoStudio software, considering variations in soil cohesion (10–80 kPa), internal friction angle (10°–40°), and unit weight (16–20 kN/m3). The PINN architecture employed three hidden dense layers with ReLU activation, optimized over 50 epochs, while XGBoost utilized metaheuristic algorithms to fine-tune hyperparameters and provide feature importance analysis. Model performance was evaluated using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Coefficient of Determination (R2). The proposed hybrid PINN-XGBoost model achieved an MAE of 0.039, RMSE of 0.060, and an R2 of 0.998 on testing data, outperforming standalone PINN (MAE = 0.116, R2 = 0.990) and traditional Multiple Linear Regression (R2 = 0.773). Feature importance analysis revealed that topsoil cohesion and unit weight were the most influential parameters, contributing 42% and 35% to model predictions, respectively. Unlike prior studies where PINN and XGBoost are applied independently, this research introduces a coupled framework that embeds physical constraints into the AI learning process while ensuring model transparency through explainable feature ranking. The integration of physics-based numerical modelling and data-driven AI significantly enhances prediction reliability, providing a practical tool for the design and safety assessment of cantilever retaining walls.</p>