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

arXiv: https://arxiv.org/abs/2606.00949 · HTML: https://mlsanity.com/paper/2606.00949/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL with diffusion and flow models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 31 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL with diffusion and flow models](https://mlsanity.com/deeprl/rl-with-diffusion-and-flow-models/)

## Builds on (most cited first, 8 of 8)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Effective control of two-dimensional Rayleigh--B'enard convection: invariant multi-agent reinforcement learning is all you need](https://mlsanity.com/paper/2304.02370/) (2023)
- [Identifying regions of importance in wall-bounded turbulence through explainable deep learning](https://mlsanity.com/paper/2302.01250/) (2023)
- [Navigation in a simplified Urban Flow through Deep Reinforcement Learning](https://mlsanity.com/paper/2409.17922/) (2024)
- [Additive-feature-attribution methods: a review on explainable artificial intelligence for fluid dynamics and heat transfer](https://mlsanity.com/paper/2409.11992/) (2024)

## Abstract (arXiv)

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.