Exploring Methods for Quantifying Uncertainty in Neural Network-Based Turbulence Closures

Machine Learning (ML) is a very promising field for data-driven modeling of different phenomena. In the field of Computational Fluid Dynamics (CFD), ML is an enticing alternative to traditional methods to improve the accuracy and computational efficiency of simulations. However, many ML models, like Neural Networks, don’t quantify their uncertainty or indicate their confidence in a prediction to those who wish to use them. This is especially important because the use of inaccurate ML predictions in a CFD simulation can greatly impact the validity of a simulation. However, with uncertainty quantification, an ML model can indicate to a modeler the confidence in its prediction, which allows the modeler to revert to more principled methods when the ML model has low confidence. The uncertainty of an ML model can be broken into Epistemic (model) and Aleatoric (data) uncertainty. Or uncertainty that stems from using an ML model to approximate a phenomena (Epistemic) and the uncertainty in the measurements that help train the ML model (Aleatoric). This study explores three UQ methods that apply to Neural Networks and one traditional method that gives more mathematically guaranteed UQ. For the Neural Networks, the UQ is done using Bayesian Inference, of which this study explores Deep Ensembles (DE), Monte-Carlo Dropout (MC-Dropout), and Stochastic Variational Inference (SVI). For the traditional methods, this study employs an exact and approximate Gaussian Process. Each of these UQ methods is then applied to synthetic turbulence closure data from [1] in order to compare their prediction and UQ accuracy.