Data-Driven Turbulence Modelling for Two- Dimensional Barotropic Flow Using Neural Networks

Abstract:

Traditional physical parameterization can be efficient and understandable, however, its oversimplification may introduce some limitation when simulating real-world atmospheric dynamics. Researchers have started to explore data-based parameterization approaches with machine learning techniques to limit the numerical error. In this work, we present a neural-network based framework for turbulence closures and deploy it for modeling the subgrid-scale (SGS) turbulence flux in a 2-D inviscid barotropic flow. We design and train neural networks based on high resolution data from direct numerical simulations (DNS) with a random initial condition. We show that the selection of other physical information, such as some of well established eddy viscosity hypothesis, as part of training input might improve training results. We discuss the time and spatial dependence of data-driven turbulence modeling through a time series prediction and a spatial structural characteristic based prediction by Recurrent Neural Networks (RNN) and Convolutional Neural Networks (CNN) respectively. In addition to traditional l2 loss function, we investigate the application of Multi-Scale Structural Similarity Index (MS-SSIM) based loss function, which improves the performance of CNN models. The performance of our neural network models are compared with the Dynamic Reconstruction Model (DRM) and evaluated by probability based validations as well as the spatial distribution of SGS fluxes. We further discuss the generalization ability of the neural network models by testing them on the Kelvin-Helmholtz instability, which is significantly different from the training dataset. In this process, we use Transfer Learning (TL) technique to improve the performance of neural network models on a new fluid field. This work represents the promising potential to develop atmospheric numerical models with data-driven machine learning algorithms to improve the performance of weather forecast and climate change prediction.