Causally-Relevant Structures in Turbulence Revealed by Explainable Deep Learning

We present a novel data-driven framework that identifies flow structures essential for the sustainment of turbulence and demonstrates their use for effective control. A 3D U-Net is trained to forecast the evolution of turbulent channel flow at a friction Reynolds number of 550, and gradient SHAP (a method from explainable deep learning) is applied to reveal the spatial regions most influential to the predictions of the network. These regions are interpreted as causally relevant, as they directly affect the ability of the model to predict future flow states. Interestingly, the high-SHAP regions identified by this method differ significantly from classical coherent structures such as Q events, streaks or vortices, suggesting that traditional turbulence paradigms may overlook key features in the dynamics. To assess the control potential of these findings, we use the SHAP importance maps to design and guide actuation strategies. In particular, we implement reinforcement-learning-based controllers that learn to selectively dampen the activity within the SHAP-identified regions. These controllers outperform standard actuation approaches that target classical structures, leading to enhanced drag reduction with lower energy input. This demonstrates that XAI tools not only help uncover novel physics of turbulence, but also enable more effective and targeted flow control. This two-step methodology (first identifying causally-important structures via explainability, then targeting them for control) represents a paradigm shift in turbulence research. It opens promising new pathways for energy-efficient flow manipulation of wall-bounded flows and provides deeper insight into the underlying mechanisms that sustain turbulence.