General-purpose data-driven wall model: Interpretability & Uncertainty

Data-driven wall models are increasingly used in wall-modeled large eddy simulations (WMLES) of turbulent flows. However, interpreting their predictions and assessing their reliability remain critical, particularly when these models are deployed across varying flow conditions in real-world applications. We present a data-driven approach that enhances both interpretability and uncertainty quantification for wall models. The method comprises four components: a baseline wall model, an error model, a classifier, and a confidence score. The baseline model is trained on representative building-block flows and predicts wall shear stress. The error model explicitly learns corrections to the baseline predictions in low-performance regions by identifying both epistemic errors (stemming from a lack of representative training cases) and aleatoric errors (arising from noise or variability in the training data). Under the right conditions, the baseline model is corrected by the error model, enabling additive learning without retraining or overfitting. The classifier predicts the probability that a test point belongs to a particular class in the training set. Finally, the confidence score quantifies the proximity of the test input to the training distribution in input space. By disentangling different sources of error and providing class probabilities and confidence estimates, the method enables informed assessment of model reliability and predictive performance at inference time. It also facilitates practical applications such as adaptive mesh refinement in WMLES.