Interpretable multiscale data-driven subgrid-scale model for wall-bounded turbulence

In this study, we developed an interpretable data-driven subgrid-scale (SGS) model for wall-bounded turbulent flow using a multiscale convolutional neural network (CNN). While data-driven SGS closures have achieved high accuracy in turbulent flow simulations, such models often lacked physical interpretability due to their black-box nature, making their predictions difficult to interpret. To address this, we quantified the contribution of each input feature to the prediction of the SGS stress components (τ_{ij})​ and demonstrated that Gradient SHapley Additive exPlanations (Gradient SHAP) provided valuable insights. The SHAP results revealed that the wall-normal gradient of streamwise velocity was the most influential feature, reflecting the dominant shear in wall-bounded turbulence. Furthermore, the data-driven SGS model exhibited qualitative agreement with classical mixed SGS models, particularly the Gradient model and Prandtl's mixing-length. These findings offer a pathway toward an interpretable data-driven SGS model in LES wall-bounded flows.