Empirical Discovery of Multi-Scale Transfer of Information in Dynamical Systems

Abstract

In this work, we quantify the time scales and information flow associated with multiscale energy transfer in a weakly turbulent system. This is done through a greedy optimization algorithm which finds the maximum conditional-mutual information across lagged embeddings of time series localized by wavenumber. For our chosen weakly turbulent system, the algorithm finds asymmetries in the information flow across wavenumbers, reflecting what are typically described as forward and inverse cascades. However, our approach goes beyond typical heuristic arguments and provides quantitative insight into the intricate multi-wave mixing dynamics necessary to maintain the steady statistical state characterizing weak turbulence. Our work then provides a novel, detailed, and fully nonlinear statistical analysis of a weakly turbulent system. The flexibility of our approach points to broader applicability in real-world data coming from chaotic or turbulent dynamical systems.