Revealing the state space of turbulence using machine learning

Abstract

We train deep convolutional autoencoders to learn highly efficient embeddings of two-dimensional turbulence. We define a new technique, latent Fourier analysis, that decomposes these representations into a set of interpretable recurrent patterns, and show how these recurrent patterns are closely related to the simple invariant solutions populating the turbulent attractor. By examining a series of bursting episodes with this framework we are able to identify large numbers of new simple invariant solutions that characterize these events and which have avoided previous detection methods.