Evaluation of exit gradient of hydraulic structures with cut-off walls in explainable machine learning surrogate based on numerical models

Abstract

We develop machine learning surrogate models based on XGBoost to predict the exit gradients that are critical in optimizing hydraulic structure design and overcoming limitations of analytical methods regarding anisotropy and boundary effects. For the XGBoost model, we use 8000 MODFLOW numerical simulations covering diverse parameters affecting groundwater flow under hydraulic structures, including anisotropy, head differentials, structure width, cut-off wall depth, aquifer thickness, and uninterrupted riverbed length. We train 60% of the MODFLOW models with a coefficient of determination above 0.99. Upon cross validating, the coefficient of determination across ten splits of training data was 0.71 indicating minimal overfitting. The coefficient of determination for test data is 0.88 demonstrating reliable exit gradient prediction by the XGBoost. For explainability of the XGBoost model, we implement the SHAP (SHapley Additive exPlanations) framework. Feature selection using the SHAP values identify the anisotropy and the ratio of cut-off wall depth to aquifer thickness as the primary influencers on the exit gradients. Notably, anisotropy's impact is more pronounced when the cut-off wall is relatively smaller compared to the hydraulic structure's width. Additionally, the influence of cut-off wall depth diminishes with higher vertical anisotropy. This analysis enhances understanding of exit gradient control factors and establishing subsurface anisotropy as a crucial factor in hydraulic structure designs regarding the exit gradient.