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

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.

arXiv comment47 pages, 21 figures, Accepted to the Journal of Computational Physics

References in corpus (6)

• Weight Uncertainty in Neural Networks
• Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
• Variational Dropout and the Local Reparameterization Trick
• Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations: A Data-Driven, Physics-Based Bayesian Approach
• Stein Variational Gradient Descent as Gradient Flow
• A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling

Cited by in corpus (30)

• A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Deep Neural Networks for Data-Driven Turbulence Models
• Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks
• Physics-informed deep learning for incompressible laminar flows
• RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
• Probabilistic neural networks for fluid flow surrogate modeling and data recovery
• Physics-guided deep learning framework for predictive modeling of the Reynolds stress anisotropy
• Generalization techniques of neural networks for fluid flow estimation
• Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network
• Solving inverse problems using conditional invertible neural networks
• Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D
• Turbulence closure modeling with data-driven techniques: physical compatibility and consistency considerations
• Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains
• An advanced hybrid deep adversarial autoencoder for parameterized nonlinear fluid flow modelling
• Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models
• State estimation with limited sensors -- A deep learning based approach
• Predicting waves in fluids with deep neural network
• Data-Driven Discovery of Coarse-Grained Equations
• Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections
• Uncertainty Quantification for Data-driven Turbulence Modelling with Mondrian Forests
• towards a robust detection of viscous and turbulent flow regions using unsupervised machine learning
• Using Machine Learning at Scale in HPC Simulations with SmartSim: An Application to Ocean Climate Modeling
• Review of Physics-based and Data-driven Multiscale Simulation Methods for Computational Fluid Dynamics and Nuclear Thermal Hydraulics
• Learning Incompressible Fluid Dynamics from Scratch -- Towards Fast, Differentiable Fluid Models that Generalize
• A Bayesian Multiscale Deep Learning Framework for Flows in Random Media
• Review and Examination of Input Feature Preparation Methods and Machine Learning Models for Turbulence Modeling
• Graph Laplacian-based Bayesian Multi-fidelity Modeling
• Turbulence closure modeling with data-driven techniques: Investigation of generalizable deep neural networks
• Data-driven quantification of model-form uncertainty in Reynolds-averaged simulations of wind farms