# Explainable deep learning reveals the physical mechanisms behind the turbulent kinetic energy equation

arXiv: https://arxiv.org/abs/2601.20052 · HTML: https://mlsanity.com/paper/2601.20052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [A Sufficient Condition for Convergences of Adam and RMSProp](https://mlsanity.com/paper/1811.09358/) (2018)
- [Synthetic Lagrangian Turbulence by Generative Diffusion Models](https://mlsanity.com/paper/2307.08529/) (2023)
- [Identifying regions of importance in wall-bounded turbulence through explainable deep learning](https://mlsanity.com/paper/2302.01250/) (2023)

## Abstract (arXiv)

In this work, we investigate the physical mechanisms governing turbulent kinetic energy transport using explainable deep learning (XDL). An XDL model based on SHapley Additive exPlanations (SHAP) is used to identify and percolate high-importance structures for the evolution of the turbulent kinetic energy budget terms of a turbulent channel flow at a friction Reynolds number of Reτ = 125. The results show that the important structures are predominantly located in the near-wall region and are more frequently associated with sweep-type events. In the viscous layer, the SHAP structures relevant for production and viscous diffusion are almost entirely contained within those relevant for dissipation, revealing a clear hierarchical organization of near-wall turbulence. In the outer layer, this hierarchical organization breaks down and only velocity-pressure-gradient correlation and turbulent transport SHAP structures remain, with a moderate spatial coincidence of approximately 60%. Finally, we show that none of the coherent structures classically studied in turbulence are capable of representing the mechanisms behind the various terms of the turbulent kinetic energy budget throughout the channel. These results reveal dissipation as the dominant organizing mechanism of near-wall turbulence, constraining production and viscous diffusion within a single structural hierarchy that breaks down in the outer layer.