Title: Interpretable Deep Reinforcement Learning Uncovers Energy-Optimized Strategies for Turbulent Drag Mitigation

Abstract:

This study introduces a novel framework that integrates Multi-Agent Deep Reinforcement Learning (MARL) with eXplainable Deep Learning (XDL) to mitigate drag in wall-bounded turbulent flows. To evaluate the efficacy of this approach, we benchmarked three distinct SHAP-guided methodologies against standard baselines, which involved training agents to directly target wall-shear stress and opposition control.

The three proposed strategies differed in how their rewards were calculated using SHAP attributions from U-net models: 1. Velocity Prediction: The reward was derived from SHAP attributions of a U-net forecasting the future velocity field. 2. Skin-Friction Prediction: The reward was based on SHAP attributions from a U-net estimating the skin-friction coefficient. 3. Combined Prediction: The reward utilized a synthesis of SHAP attributions from two separate U-nets, one predicting the skin-friction coefficient and the other forecasting wall pressure fluctuations.

The third strategy, which combined SHAP attributions for both skin-friction coefficient and wall-pressure fluctuations, demonstrated superior overall performance. It achieved a drag reduction (DR) of 34.44% and a net energy saving (NES) of 34.01%, requiring a normalized input power of merely 0.43%. When compared to opposition control, this approach yielded increases of 49.41% in drag reduction and 48.52% in net energy savings. Furthermore, relative to the direct wall-shear-stress baseline, the proposed method not only enhanced performance but also drastically lowered the normalized actuation cost from 5.90% to 0.43%.

Insights from the analysis indicate that the resulting energy-efficient policy aligns with pressure-gated actuation. The system primarily activates when wall pressure is near zero and operates on a temporal scale similar to the lifespan of near-wall turbulent structures.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC