Explainable deep reinforcement learning reveals energy-efficient control strategies for turbulent drag reduction

2026-05-30

AI Summary

This study addresses the challenge of achieving energy-efficient drag reduction in wall-bounded turbulence by proposing a novel approach that integrates multi-agent deep reinforcement learning (MARL) with interpretable deep learning. Leveraging SHAP-based attribution analysis of a U-Net model, the authors construct a physics-informed reward function—marking the first incorporation of interpretability into reinforcement learning reward design—to guide agents toward low-power control strategies grounded in wall shear stress and pressure fluctuations. The work uncovers an efficient drag-reduction mechanism termed “near-zero wall pressure-triggered intermittent actuation,” which achieves a 34.44% drag reduction and 34.01% net energy saving at a remarkably low normalized input power of only 0.43%, yielding nearly a 50% improvement in overall efficiency compared to conventional methods.

Abstract

We propose a method combining Multi-Agent Deep Reinforcement Learning (MARL) and eXplainable Deep Learning (XDL) to reduce drag in wall-bounded turbulent flows. Taking as a baseline the results of training agents directly targeting wall-shear stress and opposition control, three SHAP-guided approaches are compared. In the first, the reward is computed from SHAP attributions of a U-net predicting the future velocity field; in the second, from SHAP attributions of a U-net predicting the skin-friction coefficient; in the third, from a combination of SHAP attributions of two U-nets predicting the skin-friction coefficient and the wall pressure fluctuations, respectively. The combined SHAP strategy based on skin-friction coefficient and wall-pressure fluctuations achieves the best overall performance, achieving a DR of 34.44% and a NES of 34.01% with only 0.43% normalized input power. Relative to opposition control, drag reduction and net energy saving increase by 49.41% and 48.52%, respectively. Compared with the direct wall-shear-stress baseline, the proposed strategy simultaneously improves performance while reducing the normalized actuation cost from 5.90% to 0.43%. Analysis of the results reveals that the energetically efficient policy is consistent with pressure-gated actuation, activating predominantly at near-zero wall pressure, and operates on a temporal timescale comparable to the lifetime of the near-wall turbulent structures.

Problem

• turbulent drag reduction
• energy-efficient control
• wall-bounded turbulence
• net energy saving
• actuation cost

Innovation

• Explainable Deep Reinforcement Learning
• SHAP attribution
• Turbulent drag reduction
• Multi-Agent Reinforcement Learning
• Energy-efficient control