Causality-informed dynamic mode decomposition for unsteady flow analysis

Abstract

Causal analysis characterizes directional dependencies in dynamical systems, while such information is not typically used to inform reduced-order modeling of unsteady flows. This study proposes a Granger Causality-informed Dynamic Mode Decomposition (GC-DMD) framework that incorporates such information into data-driven modeling and modal analysis of high-dimensional flow data. The framework uses conditional Granger causality estimates to regularize the identification of the DMD operator, preferentially suppressing weakly supported interactions while preserving dynamically relevant couplings. This regularization promotes sparse operators informed by directional predictive dependencies, leading to improved predictive accuracy and identification of dynamically relevant modes. GC-DMD is evaluated on a linear system with a known coupling structure, lid-driven cavity flows with varying dynamical complexity, and a broadband transonic turbulent jet. Compared with standard DMD, GC-DMD improves operator identification accuracy in the linear benchmark and improves the robustness of the identified spectrum while reducing long-horizon prediction errors in the cavity flows. For the turbulent jet, it yields a sparser operator with improved prediction accuracy. These results demonstrate the potential of incorporating causality information to guide the identification of sparse, predictive reduced-order models of complex flows. The \href{https://github.com/JiaqingKou/GC-DMD-Granger-Causality-informed-DMD}{source codes} \footnote{https://github.com/JiaqingKou/GC-DMD-Granger-Causality-informed-DMD} from this research are publicly available in the GitHub repository.