Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks

By Nicholas Geneva, Nicholas Zabaras. 2018

141 citations recorded by the source corpus.

Abstract Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier–Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a new area of black-box turbulence models allowing for the tuning of RANS simulations to increase their predictive accuracy. While several data-driven turbulence models have been reported, the quantification of the uncertainties introduced has mostly been neglected. Uncertainty quantification for such data-driven models is essential since their predictive capability rapidly declines as they are tested for flow physics that deviate from that in the training data. In this work, we propose a novel data-driven framework that not only improves RANS predictions but also provides probabilistic bounds for fluid quantities such as velocity and pressure. The uncertainties capture both model form uncertainty as well as epistemic uncertainty induced by the limited training data. An invariant Bayesian deep neural network is used to predict the anisotropic tensor component of the Reynolds stress. This model is trained using Stein variational gradient decent algorithm. The computed uncertainty on the Reynolds stress is propagated to the quantities of interest by vanilla Monte Carlo simulation. Results are presented for two test cases that differ geometrically from the training flows at several different Reynolds numbers. The prediction enhancement of the data-driven model is discussed as well as the associated probabilistic bounds for flow properties of interest. Ultimately this framework allows for a quantitative measurement of model confidence and uncertainty quantification for flows in which no high-fidelity observations or prior knowledge is available.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges (2020, background): “[458] presented a new data-driven approach to provide probabilistic bounds for fluid quantities and enhanced RANS predictions.”
Physics-informed deep learning for incompressible laminar flows (2020, unknown): “, see [3, 4, 7]).”
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks (2019, methodology): “Among the most popular deep learning models is deep neural networks (DNNs), which have proven to be an extremely effective method for modeling a wide spectrum of physical systems such as flow through porous media [2, 3, 4], Navier-Stokes equations [5], turbulence modeling [6], molecular dynamics [7]”