Deep learning of turbulent velocity signals

We investigate the capability of a state-of-the-art deep neural model at learning features of turbulent velocity signals. Deep neural network (DNN) models are at the center of the present machine learning revolution. The set of complex tasks in which they over perform human capabilities and best algorithmic solutions grows at an impressive rate and includes, but it is not limited to, image, video and language analysis, automated control, and even life science modeling. Besides, deep learning is receiving increasing attention in connection to a vast set of problems in physics where quantitatively accurate outcomes are expected.

We consider turbulent velocity signals, spanning decades in Reynolds numbers, which have been generated via shell models for the turbulent energy cascade. Given the multi-scale nature of the turbulent signals, we focus on the fundamental question of whether a deep neural network (DNN) is capable of learning, after supervised training with very high statistics, feature extractors to address and distinguish intermittent and multi-scale signals. Can the DNN measure the Reynolds number of the signals? Which feature is the DNN learning?