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Physics-guided Bayesian neural networks for zonal corrections and uncertainty quantification in separated flows

Ali Eidi, Tyler Buchanan, Letian Jiang, Richard P. Dwight

TL;DR

The paper tackles the challenge of accurate RANS predictions for separated flows by introducing a tensor-basis Bayesian neural network that learns corrections to Reynolds stress anisotropy and TKE production. It implements a RITA-based zonal classifier to apply corrections selectively in shear-dominated regions, enabling physically consistent updates and uncertainty propagation into the flow solution. The approach demonstrates improved mean predictions and meaningful uncertainty quantification on benchmark cases, with aleatoric uncertainty dominating due to data sparsity. This method provides a principled way to couple data-driven corrections with physics-based turbulence models, potentially enhancing reliability across geometries with similar topologies and guiding future 3D extensions.

Abstract

Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions. Existing approaches often struggle with generalization beyond training cases and lack robust uncertainty quantification frameworks, limiting their utility in complex flow regimes. We propose a Bayesian neural network (BNN)-based framework specifically designed for two-dimensional separated flows. By focusing on flow zones near separated regions, we ensure targeted training and enhance predictive reliability. The BNN framework incorporates physics-guided, invariant inputs to maintain consistency with turbulence physics. Correction terms predicted by the BNN are selectively applied to specific regions of the flow domain using a novel classifier, improving accuracy. A key feature of this approach is propagating BNN-derived corrections to flow solutions, enabling uncertainty quantification in unseen test cases. This probabilistic characterization of modeling errors offers insights into the reliability of RANS predictions across geometries with similar topologies. Preliminary results demonstrate that this method accurately predicts correction terms for Reynolds stress anisotropy and turbulent kinetic energy production in separated flow regions, effectively addressing dominant modeling errors and advancing turbulence modeling through uncertainty quantification.

Physics-guided Bayesian neural networks for zonal corrections and uncertainty quantification in separated flows

TL;DR

The paper tackles the challenge of accurate RANS predictions for separated flows by introducing a tensor-basis Bayesian neural network that learns corrections to Reynolds stress anisotropy and TKE production. It implements a RITA-based zonal classifier to apply corrections selectively in shear-dominated regions, enabling physically consistent updates and uncertainty propagation into the flow solution. The approach demonstrates improved mean predictions and meaningful uncertainty quantification on benchmark cases, with aleatoric uncertainty dominating due to data sparsity. This method provides a principled way to couple data-driven corrections with physics-based turbulence models, potentially enhancing reliability across geometries with similar topologies and guiding future 3D extensions.

Abstract

Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions. Existing approaches often struggle with generalization beyond training cases and lack robust uncertainty quantification frameworks, limiting their utility in complex flow regimes. We propose a Bayesian neural network (BNN)-based framework specifically designed for two-dimensional separated flows. By focusing on flow zones near separated regions, we ensure targeted training and enhance predictive reliability. The BNN framework incorporates physics-guided, invariant inputs to maintain consistency with turbulence physics. Correction terms predicted by the BNN are selectively applied to specific regions of the flow domain using a novel classifier, improving accuracy. A key feature of this approach is propagating BNN-derived corrections to flow solutions, enabling uncertainty quantification in unseen test cases. This probabilistic characterization of modeling errors offers insights into the reliability of RANS predictions across geometries with similar topologies. Preliminary results demonstrate that this method accurately predicts correction terms for Reynolds stress anisotropy and turbulent kinetic energy production in separated flow regions, effectively addressing dominant modeling errors and advancing turbulence modeling through uncertainty quantification.

Paper Structure

This paper contains 10 sections, 10 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Bayesian neural networks
  4. Turbulence model correction
  5. Zonal classification
  6. Results and Discussion
  7. BNN structure and UQ framework
  8. Inference
  9. Propagation
  10. Conclusion

Figures (3)

  • Figure 1: Tensor-basis BNN structure for TKE production correction
  • Figure 2: Error metrics for training and test data with uncertainty values for TKE production: training data with epistemic uncertainty (a), training data with aleatoric uncertainty (b), test data with epistemic uncertainty (c) and test data with aleatoric uncertainty (d).
  • Figure 3: Normalized velocity (a) and TKE (b) profiles for one of the test cases, showing baseline predictions, high-fidelity (HF) data, shear layer (SL) correction propagation, and BNN mean prediction propagation results, along with aleatoric and epistemic uncertainty bounds.