Adaptive Model Refinement Approach for Bayesian Uncertainty Quantification in Turbulence Model

Zeng, Fangfang; Zhang, Wei; Li, Jinping; Zhang, Tianxin; Yan, Chao

doi:10.2514/1.j060889

Cited by 14 publications

(3 citation statements)

References 39 publications

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“…Furthermore, Xie et al [10] combined IUQ and quantitative validation via Bayesian hypothesis testing to improve the predictive capability of computer simulations. Besides the applications in nuclear energy, the Bayesian approach for IUQ has also been applied to many other fields such as biotechnology [11], geophysics [12], additive manufacturing [13], computational fluid dynamics [14,15], etc.…”

Section: Introductionmentioning

confidence: 99%

Scalable Inverse Uncertainty Quantification by Hierarchical Bayesian Modeling and Variational Inference

Wang,

Wu,

Xie

et al. 2023

Energies

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Inverse Uncertainty Quantification (IUQ) has gained increasing attention in the field of nuclear engineering, especially nuclear thermal-hydraulics (TH), where it serves as an important tool for quantifying the uncertainties in the physical model parameters (PMPs) while making the model predictions consistent with the experimental data. In this paper, we present an extension to an existing Bayesian inference-based IUQ methodology by employing a hierarchical Bayesian model and variational inference (VI), and apply this novel framework to a real-world nuclear TH scenario. The proposed approach leverages a hierarchical model to encapsulate group-level behaviors inherent to the PMPs, thereby mitigating existing challenges posed by the high variability of PMPs under diverse experimental conditions and the potential overfitting issues due to unknown model discrepancies or outliers. To accommodate computational scalability and efficiency, we utilize VI to enable the framework to be used in applications with a large number of variables or datasets. The efficacy of the proposed method is evaluated against a previous study where a No-U-Turn-Sampler was used in a Bayesian hierarchical model. We illustrate the performance comparisons of the proposed framework through a synthetic data example and an applied case in nuclear TH. Our findings reveal that the presented approach not only delivers accurate and efficient IUQ without the need for manual tuning, but also offers a promising way for scaling to larger, more complex nuclear TH experimental datasets.

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Section: Introductionmentioning

confidence: 99%

Scalable Inverse Uncertainty Quantification by Hierarchical Bayesian Modeling and Variational Inference

Wang,

Wu,

Xie

et al. 2023

Energies

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show abstract

“…This is often experience-based, which usually introduces the maximum and minimum magnitude of perturbation, resulting in overly conservative perturbations [3,6,11]. Recent machine Learning models can estimate RANS model uncertainty with improved accuracy [12][13][14][15][16][17][18][19][20]; however, they are often complex and demand a large size of training data. Complex machine learning models not only require additional computational resources in training but also become less comprehensive to researchers.…”

Section: Introductionmentioning

confidence: 99%

Machine learning based uncertainty quantification of turbulence model for airfoils

Minghan¹,

Qian²

2022

Preprint

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Reynolds-averaged Navier-Stokes (RANS)-based transition modeling is widely used in aerospace applications but suffers inaccuracies due to the Boussinesq turbulent viscosity hypothesis. The eigenspace perturbation method can estimate the accuracy of a RANS model by injecting perturbations to its predicted Reynolds stresses. However, there lacks a reliable method for choosing the strength of the injected perturbation, while existing machine learning models are often complex and data craving. We examined two light-weighted machine learning models to help select the strength of the injected perturbation for estimating the RANS uncertainty of flows undergoing the transition to turbulence over a Selig-Donovan 7003 airfoil. On the one hand, we examined polynomial regression to construct a marker function augmented with eigenvalue perturbations to estimate the uncertainty bound for the predicted skin friction coefficient. On the other hand, we trained a convolutional neural network (CNN) to predict high-fidelity turbulence kinetic energy. The trained CNN acts as a marker function that can be integrated into the eigenspace perturbation method to quantify the RANS uncertainty. Our findings suggest that the light-weighted machine learning models are effective in constructing an appropriate marker function that is promising to enrich the existing eigenspace perturbation method to quantify the RANS uncertainty more precisely.

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“…Machine Learning based approaches are becoming more used in fluid mechanics applications (Duraisamy et al, 2019;Chung et al, 2021;Brunton et al, 2020). Some prior investigators have tried to use ML to improve turbulence model UQ (Xiao et al, 2016;Wu et al, 2018;Heyse et al, 2021b;a;Zeng et al, 2022). These studies have focused on more complex models that necessitate large incorporation of labeled data and limit generalizability.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Methods

Chu¹

2021

Uncertainty Quantification of Stochastic Defects in Materials

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Reliable prediction of turbulent flows is an important necessity across different fields of science and engineering. In Computational Fluid Dynamics (CFD) simulations, the most common type of models are eddy viscosity models that are computationally inexpensive but introduce a high degree of epistemic error. The Eigenspace Perturbation Method (EPM) attempts to quantify this predictive uncertainty via physics based perturbation in the spectral representation of the predictions. While the EPM outlines how to perturb, it does not address how much or even where to perturb. We address this need by introducing machine learning models to predict the details of the perturbation, thus creating a physics inspired machine learning (ML) based perturbation framework. In our choice of ML models, we focus on incorporating physics based inductive biases while retaining computational economy. Specifically we use a Convolutional Neural Network (CNN) to learn the correction between turbulence model predictions and true results. This physics inspired machine learning based perturbation approach is able to modulate the intensity and location of perturbations and leads to improved estimates of turbulence model errors.

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Adaptive Model Refinement Approach for Bayesian Uncertainty Quantification in Turbulence Model

Cited by 14 publications

References 39 publications

Scalable Inverse Uncertainty Quantification by Hierarchical Bayesian Modeling and Variational Inference

Scalable Inverse Uncertainty Quantification by Hierarchical Bayesian Modeling and Variational Inference

Machine learning based uncertainty quantification of turbulence model for airfoils

Machine Learning Methods

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