In the present study, we investigate different data-driven parameterizations for large eddy simulation of two-dimensional turbulence in the a priori settings. These models utilize resolved flow field variables on the coarser grid to estimate the subgrid-scale stresses. We use data-driven closure models based on localized learning that employs a multilayer feedforward artificial neural network with point-to-point mapping and neighboring stencil data mapping, and convolutional neural network fed by data snapshots of the whole domain. The performance of these data-driven closure models is measured through a probability density function and is compared with the dynamic Smagorinsky model (DSM). The quantitative performance is evaluated using the cross-correlation coefficient between the true and predicted stresses. We analyze different frameworks in terms of the amount of training data, selection of input and output features, their characteristics in modeling with accuracy, and training and deployment computational time. We also demonstrate computational gain that can be achieved using the intelligent eddy viscosity model that learns eddy viscosity computed by the DSM instead of subgrid-scale stresses. We detail the hyperparameters optimization of these models using the grid search algorithm.

中文翻译：

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Kraichnan湍流亚网格尺度参数化深度学习的先验分析

在本研究中，我们研究了不同的数据驱动参数化，用于先验设置中二维湍流的大涡模拟。这些模型利用粗网格上的解析流场变量来估计亚网格尺度的应力。我们使用基于局部学习的数据驱动闭包模型，该模型采用具有点对点映射和相邻模板数据映射的多层前馈人工神经网络，以及由整个域的数据快照馈送的卷积神经网络。这些数据驱动的闭合模型的性能通过概率密度函数进行测量，并与动态 Smagorinsky 模型 (DSM) 进行比较。使用真实应力和预测应力之间的互相关系数来评估定量性能。我们在训练数据量、输入和输出特征的选择、它们在准确建模方面的特征以及训练和部署计算时间方面分析了不同的框架。我们还展示了使用智能涡粘性模型可以实现的计算增益，该模型学习由 DSM 计算的涡粘性，而不是亚网格尺度应力。我们使用网格搜索算法详细介绍了这些模型的超参数优化。