Quantifying Model Uncertainty of Neural-Network based Turbulence Closures

With increasing computational demand, Neural-Network (NN) based models are being developed as pre-trained 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 uncertainties 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 [1]. The uncertainty quantification (UQ) methods explored are Deep Ensembles, Monte-Carlo 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, paper finds Deep Ensembles have the best prediction accuracy with an RMSE of 4.31 · 10⁻⁴ on the testing inputs followed by Monte-Carlo Dropout and Stochastic Variational Inference. For uncertainty quantification, this paper finds each method produces unique Epistemic uncertainty estimates with Deep Ensembles being overconfident in regions, MC-Dropout being under-confident, and SVI producing principled uncertainty at the cost of function diversity.