A Grey Wolf Optimized Deep Learning Framework for Robust Prediction of Subgrade Resilient Modulus

The precise calculation of the resilient modulus (M _R ) of compacted subgrade soil is a crucial step in designing safe and sustainable flexible pavement systems. The M _R is a key parameter governing the structural performance of pavements under repeated traffic loading. The proposed research investigates the applicability of nature-inspired, population-based metaheuristic swarm intelligence algorithms for estimating the M _R of pavement subgrade soil. A dataset comprising 2,813 samples was systematically divided into training and testing subsets, considering important soil, stress, moisture, and environmental variables. Three widely used machine learning (ML) models - Multivariate Adaptive Regression Splines (MARS), Extreme Learning Machine (ELM), and Deep Neural Network (DNN) - were developed to predict M _R values. To further improve prediction accuracy, a swarm intelligence-based approach, namely the Grey Wolf Optimizer (GWO), was employed to optimize and combine the outputs of the independent ML models. The reliability and robustness of the developed models were evaluated using 10-fold cross-validation, Shapley Additive Explanation (SHAP) analysis, partial dependence plots (PDP), and error box plots. The generalization capability of the proposed models was additionally assessed using an independent experimental dataset consisting of 40 M _R specimens. The results demonstrate that the GWO-DNN model outperformed the other algorithms, achieving the highest prediction accuracy with an R² value of 0.971 and an RMSE of 4.05 MPa. To enhance practical applicability, a graphical user interface (GUI) was developed, enabling engineers and researchers to input basic parameters and directly estimate M _R . This study contributes to data-driven advancements in geo-transportation engineering, improving the efficiency and sustainability of M _R estimation.