Deep learning based sub-grid scale closure for LES of Kraichnan turbulence*

Performing high-fidelity simulations of large scale multiscale flow problems that resolves fine spatiotemporal features is computationally intractable. Large eddy simulation (LES) tech- niques aim at reducing the computational resources by resolving large scales of the flow and the effect of small scales is modeled. In the present work, we put forth data-driven sub-grid scale closure models for LES of two-dimensional Kraichnan turbulence in the a priori settings. We use the resolved flow field on the coarser grid to estimate the eddy viscosity and subgrid-stresses. Our data-driven closure models are based on convolutional neural network (CNN) fed by snapshot data from the whole domain, and multilayer feedforward deep neural network (DNN) that utilizes localized stencil data. We analyze these two different neural networks in terms of the amount of training data, training and deployment computational time, selection of input and output features, and their characteristics in modeling accuracy and numerical stability.