A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

TL;DR

This paper evaluates data-driven neural network models for subgrid-scale stress prediction in 2D turbulence, comparing their accuracy and computational efficiency against traditional models like DSM in an a priori setting.

Contribution

It introduces and compares neural network-based closure models, including ANN and CNN, for turbulence modeling, optimizing hyperparameters and demonstrating computational gains over traditional methods.

Findings

Neural network models can accurately predict subgrid-scale stresses.

CNN models outperform ANN in capturing turbulence features.

Data-driven models offer computational advantages over traditional methods.

Abstract

In the present study, we investigate different data-driven parameterizations for large eddy simulation of two-dimensional turbulence in the \emph{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 multilayer feedforward artificial neural network (ANN) with point-to-point mapping and neighboring stencil data mapping, and convolutional neural network (CNN) 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 Smagorinksy 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.