{"ID":2922229,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-03T00:47:32.987482086Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.00949","arxiv_id":"2606.00949","title":"Explainable deep reinforcement learning reveals energy-efficient control strategies for turbulent drag reduction","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.","short_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...","url_abs":"https://arxiv.org/abs/2606.00949","url_pdf":"https://arxiv.org/pdf/2606.00949v1","authors":"[\"Federica Tonti\",\"Ricardo Vinuesa\"]","published":"2026-05-31T02:02:37Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"physics.flu-dyn\"]","methods":"[\"Reinforcement Learning\"]","has_code":false}