Neural Network Complexity of Chaos and Turbulence
This work provides a novel computational approach to measure complexity in fluid dynamics, which could aid researchers in physics and engineering, though it is incremental in applying existing neural network methods to this domain.
The study tackled the problem of quantifying the complexity of chaos and turbulence by using deep neural networks to classify images of fluid profiles, finding that the network uses the two-point correlation spectra of vorticity as a key feature for distinguishing between chaotic and turbulent regimes.
Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations, and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.