Extracting time-varying causal modes of aerodynamic flows with information-theoretic machine learning

Aerodynamicists have examined the relationship between complex flow behaviors and aerodynamic forces by analyzing time series data obtained from numerical simulations or experiments. In doing so, we aim to identify causal links --- where specific regions of the flow field (causes) influence aerodynamic responses (effects) after a certain time delay. This study considers extracting such a causal relationship using information-theoretic machine learning. The present data-driven approach enables the decomposition of a given flow field snapshot into an informative component and its non-informative counterpart with respect to a target variable at a future time stamp, thereby capturing the causality as a time-varying modal structure. We perform the present informative mode decomposition with strong gust-wing interactions of 1 .numerical and 2 .experimental measurements, and 3. a turbulent separated wake. Along with these examples covering a range of spatiotemporal aerodynamic characteristics, we discuss how the present approach extracts time-varying informative modes associated with the lift response from seemingly complex vortical structures. This study provides causality-based insights into a range of unsteady aerodynamic problems.