Bayesian neural network correction of RANS turbulence models with uncertainty quantification in separated flows

Abstract

Data-driven correction of turbulence models offers a promising route for improving Reynolds-averaged Navier-Stokes (RANS) predictions, but quantifying uncertainty in such corrections and ensuring generalization across flows remain key challenges. This work presents a Bayesian neural network (BNN) framework for uncertainty-aware correction of RANS models. The BNN represents both epistemic and input-dependent aleatoric uncertainty, interpreted here as irreducible scatter in the feature-to-correction relationship, with the latter propagated as spatially correlated fields through the RANS solver. The framework is trained exclusively on a periodic-hill configuration and evaluated without retraining on five unseen separated-flow configurations. The learned corrections improve the training-flow prediction, but the strong momentum-field benefit obtained from the anisotropy correction does not transfer consistently to the unseen flows. Out-of-distribution under-coverage is already present at the correction-field level, indicating that the loss of calibration is already present in transfer of the learned correction rather than being introduced primarily by CFD propagation. Overall, the framework enables joint propagation of epistemic and aleatoric uncertainty while exposing the present limitations of uncertainty calibration under distribution shift.