On the potential of transfer entropy in turbulent dynamical systems.

Information theory (IT) provides tools to estimate causality between events, in various scientific domains. Here, we explore the potential of IT-based causality estimation in turbulent (i.e. chaotic) dynamical systems and investigate the impact of various hyperparameters on the outcomes. The influence of Markovian orders, i.e. the time lags, on the computation of the transfer entropy (TE) has been mostly overlooked in the literature. We show that the history effect remarkably affects the TE estimation, especially for turbulent signals. In a turbulent channel flow, we compare the TE with standard measures such as auto- and cross-correlation, showing that the TE has a dominant direction, i.e. from the walls towards the core of the flow. In addition, we found that, in generic low-order vector auto-regressive models (VAR), the causality time scale is determined from the order of the VAR, rather than the integral time scale. Eventually, we propose a novel application of TE as a sensitivity measure for controlling computational errors in numerical simulations with adaptive mesh refinement. The introduced indicator is fully data-driven, no solution of adjoint equations is required, with an improved convergence to the accurate function of interest. In summary, we demonstrate the potential of TE for turbulence, where other measures may only provide partial information.