A Priori Assessment of Prediction Confidence for Data-Driven Turbulence   Modeling
  Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. Recently, a data-driven turbulence modeling approach via machine learning has been proposed to predict the Reynolds stress anisotropy of a given flow based on high fidelity data from closely related flows. In this work, the closeness of different flows is investigated to assess the prediction confidence a priori. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. The flow over periodic hills at Re=10595 is used as the test set and seven flows with different configurations are individually used as training set. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of the data source and to assess the prediction confidence for data-driven turbulence modeling. 
Jin-Long Wu, Jian-Xun Wang, Heng Xiao, Julia Ling
physics.comp-ph physics.flu-dyn