Improving turbulence control through explainable deep learning

Abstract

Turbulent-flow control aims to develop strategies that effectively manipulate fluid systems, such as the reduction of drag in transportation and enhancing energy efficiency, both critical steps towards reducing global CO$_2$ emissions. Deep reinforcement learning (DRL) offers novel tools to discover flow-control strategies, which we combine with our knowledge of the physics of turbulence. We integrate explainable deep learning (XDL) to objectively identify the coherent structures containing the most informative regions in the flow, with a DRL model trained to reduce them. The model trained with XDL targets the most relevant regions in the flow to sustain turbulence and produces a drag reduction which is higher than that of a model specifically trained to reduce the drag, resulting in a $18.1\%$ better net-energy saving. The XDL-based control remains the most effective control strategy when generalizing across Reynolds numbers and geometries. This demonstrates that combining DRL with XDL can produce causal control strategies that precisely target the most influential features of turbulence. By directly addressing the core mechanisms that sustain turbulence, our approach offers a powerful pathway towards its efficient control, which is a long-standing challenge in physics with profound implications for energy systems, climate modeling and aerodynamics.