An Explainable Deep Learning for Data-Driven Turbulence Model Feature Discovery

This work presents an explainable deep learning for turbulence modelling feature discovery in several flow configurations where conventional approaches perform poorly. The proposed neural network-based turbulence model predicts the Reynolds stress based on the mean flow quantities. Furthermore, the neural network model is enriched with SHAPley Additive Explanations (SHAP) to complement the predictive power of the neural network with explainability. Our study demonstrates that the proposed model surpasses the benchmark performance of the conventional turbulence model and tensor-based neural network on the flow in a square duct and the flow over periodic hills. Most importantly, we studied the effect of input feature selection on the model’s accuracy and conducted an importance analysis using SHAP, which corroborated the findings regarding the effect of input features in our study. The findings from explainability also underscore the significance of variables less commonly utilized in traditional turbulence modeling, such as pressure gradient and Reynolds number. These findings underscore the potential of combining the proposed network with explainability to glean insights for the development of future turbulence models. Furthermore, this study demonstrates the neural network capability that can deliver exceptional accuracy, combined with SHAP as an explainable artificial intelligence method, serving as an efficient tool for feature analysis on specific flow cases that can be implemented in various fluid dynamics problems. While the model shows excellent predictive performance, it is important to note that its reliability is limited to the specific flow cases it was trained on.