# Identifying regions of importance in wall-bounded turbulence through explainable deep learning

arXiv: https://arxiv.org/abs/2302.01250 · HTML: https://mlsanity.com/paper/2302.01250/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 79 references that are in the map.
- First posted on arXiv 2 Feb 2023.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [A Sufficient Condition for Convergences of Adam and RMSProp](https://mlsanity.com/paper/1811.09358/) (2018)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [When Explainability Meets Adversarial Learning: Detecting Adversarial Examples using SHAP Signatures](https://mlsanity.com/paper/1909.03418/) (2019)
- [RKHS-SHAP: Shapley Values for Kernel Methods](https://mlsanity.com/paper/2110.09167/) (2021)

## Built on by (most cited first, 15 of 15)

- [Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environments](https://mlsanity.com/paper/2506.00214/) (2025)
- [Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2406.03789/) (2024)
- [Additive-feature-attribution methods: a review on explainable artificial intelligence for fluid dynamics and heat transfer](https://mlsanity.com/paper/2409.11992/) (2024)
- [Explainable AI: Learning from the Learners](https://mlsanity.com/paper/2601.05525/) (2026)
- [Decoding complexity: how machine learning is redefining scientific discovery](https://mlsanity.com/paper/2405.04161/) (2024)
- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence](https://mlsanity.com/paper/2403.17993/) (2024)
- [Prediction of flow and elastic stresses in a viscoelastic turbulent channel flow using convolutional neural networks](https://mlsanity.com/paper/2404.14121/) (2024)
- [Information-theoretic machine learning for time-varying mode decomposition of separated aerodynamic flows](https://mlsanity.com/paper/2505.24132/) (2025)
- [Sparse Kalman Identification for Partially Observable Systems via Adaptive Bayesian Learning](https://mlsanity.com/paper/2511.18051/) (2025)
- [Explainable deep learning reveals the physical mechanisms behind the turbulent kinetic energy equation](https://mlsanity.com/paper/2601.20052/) (2026)
- [Physics-integrated neural differentiable modeling for immersed boundary systems](https://mlsanity.com/paper/2603.16277/) (2026)
- [Physics-guided surrogate learning enables zero-shot control of turbulent wings](https://mlsanity.com/paper/2604.09434/) (2026)
- [Explainable deep reinforcement learning reveals energy-efficient control strategies for turbulent drag reduction](https://mlsanity.com/paper/2606.00949/) (2026)
- [Weak Dominant Balance for Robust Identification of Dynamically Consistent Fluid Flow Structure](https://mlsanity.com/paper/2606.29047/) (2026)

## Abstract (arXiv)

Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such interactions are explored in this study for the first time using an explainable deep-learning method. The instantaneous velocity field obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. Based on the predicted flow, we assess the importance of each structure for this prediction using the game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work provides results in agreement with previous observations in the literature and extends them by revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify completely new structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.