Using deep learning for prediction of turbulent flow statistics at high Reynolds numbers

The turbulent motion of fluid flows is a complex, strongly non-linear, multi-scale phenomenon, which poses some of the most difficult and fundamental problems in classical physics. Turbulent flows are characterized by random spatio-temporal fluctuations over a wide range of scales. The general challenge of turbulence research is to predict the statistics of these fluctuating velocity and scalar fields. A precise and computationally affordable prediction of these statistical properties of turbulence would be of practical importance for a wide field of applications ranging from geophysics to combustion science.

Deep learning (DL) has been improved substantially in recent years and has proven to contribute to the solution of many problems in a large variety of fields. In this work, DL is used to predict statistics of turbulent flows at high Reynolds numbers. Despite the stochastic nature of turbulence, DL can be used to trace certain coherent structures and statistical symmetries exhibiting turbulence. By applying DL to highly-resolved homogeneous isotropic turbulence data, different DL strategies such as network architecture and loss functions are discussed with respect to their suitability for predicting statistics of scalar fields and the scalar dissipation rate.