Uncertainty Quantification of Separated Flows Using Bayesian Neural Networks*

Data-driven turbulence modeling has become increasingly utilized to enhance the accuracy of simulations in fluid dynamics, particularly for Reynolds-Averaged Navier–Stokes (RANS) simulations. Although traditional data-driven methods have shown promise in improving turbulence predictions, they often struggle to accurately capture complex turbulence dynamics, with uncertainty quantification generally neglected. Such quantification is crucial as the extrapolation capability of these models can significantly deteriorate when applied to Out-Of-Distribution (OOD) regimes. In response to these challenges, this work introduces a novel Relative Importance Term Analysis (RITA) approach with Bayesian Neural Networks (BNNs) to advance turbulence modeling for separated flows. BNNs offer several advantages over traditional multilayer perceptions (MLPs), including superior generalization capabilities and an intrinsic framework for capturing epistemic and aleatoric uncertainties.

The proposed framework emphasizes the precise modeling of the shear layer, a crucial component for accurate predictions of separated flows. By leveraging the strengths of BNNs, the approach aims to improve turbulence predictions and provide probabilistic bounds on uncertainties associated with these predictions. The framework's effectiveness is evaluated by comparing its performance with traditional data-driven methods and assessing its capability to manage uncertainties across different flow conditions. Integrating Bayesian deep learning techniques into turbulence modeling offers a systematic process for handling uncertainties, contributing to a better understanding of turbulence dynamics and enhancing the reliability of turbulence models for practical engineering simulations.