Neural Network Complexity of Chaos and Turbulence

We study the complexity of chaos and turbulence as viewed by deep neural networks by considering network classification tasks of distinguishing turbulent from chaotic fluid flows, noise and real world images of cats or dogs. We analyze the relative difficulty of these classification tasks and quantify the complexity of the computation at the intermediate and final stages. We analyze incompressible as well as weakly compressible fluid flows and provide evidence for the feature identified by the neural network to distinguish turbulence from chaos.