Toward Incorporating Epistemic Uncertainty of Neural Network–Based Turbulence Closures in RANS CFD Simulations

With increasing computational demand, neural network– (NN) based models are being developed as pretrained surrogates for different thermohydraulics phenomena. An area where this approach has shown promise is in developing higher-fidelity turbulence closures for computational fluid dynamics (CFD) simulations. The primary bottleneck to the widespread adaptation of these NN-based closures for nuclear engineering applications is the uncertainty associated with them. The current paper illustrates three commonly used methods that can be used to quantify model uncertainty in NN-based turbulence closures. The NN model used for the current study is trained on data from an algebraic turbulence closure model. The uncertainty quantification (UQ) methods explored are deep ensembles, Monte Carlo dropout (MC-Dropout), and stochastic variational inference (SVI). The paper ends with a discussion on the relative performance of the three methods for quantifying epistemic uncertainties of NN-based turbulence closures and potentially how they could be further extended to quantify out-of-training uncertainties. For accuracy in turbulence modeling, this research finds that deep ensembles have the best prediction accuracy, with an root mean squared error of (Formula presented.) on the testing inputs, followed by MC-Dropout and SVI. For UQ, this paper finds each that method produces unique epistemic uncertainty estimates, with deep ensembles being overconfident in regions, MC-Dropout being underconfident, and SVI producing principled uncertainty at the cost of function diversity. Finally, the paper lays out a strategy of how UQ of the NN-based turbulence closures could be incorporated into RANS CFD simulations.