Subgrid modelling for two-dimensional turbulence using neural networks
Subgrid modelling for two-dimensional turbulence using neural networks
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DOI：
10.1017/jfm.2018.770
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发表时间：
2018-08
影响因子：
3.7
通讯作者：
R. Maulik;O. San;A. Rasheed;P. Vedula
中科院分区：
文献类型：
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作者：
R. Maulik;O. San;A. Rasheed;P. Vedula
在这项研究中，引入了一个数据驱动的湍流闭合框架，并将其部署到Kraichnan湍流的子网格模型中。该方法的新颖之处在于将高保真数值数据的快照用于人工神经网络，通过局部网格分解信息预测湍流源项。特别地，我们提出的方法成功地建立了由涡度和流函数模板给出的输入之间的映射，以及来自两个著名的涡流粘度核的信息。据此，我们对亚网格涡度强迫进行了时空动态预测。我们的研究在本质上既是先验的又是后验的。在前者中，我们提出了广泛的超参数优化分析，以及通过基于概率密度函数的子网格预测验证来学习量化。在后者中，我们分析了在存在与时间和空间离散相关的误差的经典二维衰减湍流测试用例中我们的流动演化框架的性能。角平均动能谱形式的统计评估表明了所提出的子网格数量推断方法的前景。此外，还观察到，为了获得更高的精度，在最优模型选择期间必须考虑一些后验误差的度量。因此，本文的结果代表了从数据生成无启发式湍流闭包的框架形式化的一个有希望的发展。
In this investigation, a data-driven turbulence closure framework is introduced and deployed for the subgrid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the subgrid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a priori and a posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability-density-function-based validation of subgrid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for subgrid quantity inference. In addition, it is also observed that some measure of a posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data.