Enhancing machine learning turbulence models via prediction of tensor basis normalized coefficients
With the rapid advancement of machine learning techniques, their application in developing turbulence models has become increasingly prevalent. Numerous machine learning turbulence models have recently been founded on Pope's general eddy-effective hypothesis. However, most of these models direc...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
16.10.2024
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Subjects | |
Online Access | Get full text |
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Summary: | With the rapid advancement of machine learning techniques, their application
in developing turbulence models has become increasingly prevalent. Numerous
machine learning turbulence models have recently been founded on Pope's general
eddy-effective hypothesis. However, most of these models directly predict the
non-dimensional Reynolds deviatoric tensor, treating tensor basis coefficients
as intermediate variables. This approach presents three primary drawbacks.
Firstly, it conflates the training error of the machine learning regression
algorithm with the modeling error inherent in Pope's general eddy-effective
hypothesis. Secondly, by treating tensor basis coefficients as intermediary
values, researchers often overlook their significance and physical
interpretation, particularly in black-box models such as neural networks.
Thirdly, this method introduces numerical interdependence among tensor basis
coefficients, violating the orthogonality of the tensor basis. Yin et al.
(2022) proposed a neural network-based turbulence model that utilizes tensor
basis coefficients as prediction labels. However, their framework employs a
regularization method with numerous hyperparameters to achieve convergence and
smooth results by leveraging information from the linear-eddy viscosity
hypothesis. In this study, we introduce a novel approach to enhance the
accuracy and realizability of machine learning turbulence models by predicting
tensor basis normalized coefficients. This method's fundamental principle is
the normalization and bounding of prediction labels for machine learning
algorithms. Utilizing periodic hills direct numerical simulation (DNS) data for
training and testing, we demonstrate that our innovative method improves
accuracy and realizability in neural network-based and symbolic
regression-based turbulence models. |
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DOI: | 10.48550/arxiv.2410.12255 |