Assessing the information content of complex flows.

Abstract

Complex dynamical systems can potentially contain a vast amount of information. Accurately assessing how much of this information must be captured to retain the essential physics is a key step for determining appropriate discretization for numerical simulation or measurement resolution for experiments. Using recent mathematical advances, we define spatiotemporally compact objects that we term dynamical linear neighborhoods (DLNs) that reduce the amount of information needed to capture the local dynamics in a well-defined way. By solving a set-cover problem, we show that we can compress the information in a full dynamical system into a smaller set of optimally influential DLNs. We demonstrate our techniques on experimental data from a laboratory quasi-two-dimensional turbulent flow. Our results have implications both for assessments of the fidelity of simulations or experiments and for the compression of large dynamical data sets.