# A deep learning approach to wall-shear stress quantification: From numerical training to zero-shot experimental application

arXiv: https://arxiv.org/abs/2409.03933 · HTML: https://mlsanity.com/paper/2409.03933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 65 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 11 of 11)

- [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)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [Physics-informed deep-learning applications to experimental fluid mechanics](https://mlsanity.com/paper/2203.15402/) (2022)
- [Mesh convolutional neural networks for wall shear stress estimation in 3D artery models](https://mlsanity.com/paper/2109.04797/) (2021)
- [Predicting the wall-shear stress and wall pressure through convolutional neural networks](https://mlsanity.com/paper/2303.00706/) (2023)
- [Uncovering wall-shear stress dynamics from neural-network enhanced fluid flow measurements](https://mlsanity.com/paper/2310.11147/) (2023)

## Abstract (arXiv)

The accurate quantification of wall-shear stress dynamics is of substantial importance for various applications in fundamental and applied research, spanning areas from human health to aircraft design and optimization. Despite significant progress in experimental measurement techniques and post-processing algorithms, temporally resolved wall-shear stress dynamics with adequate spatial resolution and within a suitable spatial domain remain an elusive goal. To address this gap, we introduce a deep learning architecture that ingests wall-parallel velocity fields from the logarithmic layer of turbulent wall-bounded flows and outputs the corresponding 2D wall-shear stress fields with identical spatial resolution and domain size. From a physical perspective, our framework acts as a surrogate model encapsulating the various mechanisms through which highly energetic outer-layer flow structures influence the governing wall-shear stress dynamics. The network is trained in a supervised fashion on a unified dataset comprising direct numerical simulations of statistically 1D turbulent channel and spatially developing turbulent boundary layer flows at friction Reynolds numbers ranging from 390 to 1,500. We demonstrate a zero-shot applicability to experimental velocity fields obtained from Particle-Image Velocimetry measurements and verify the physical accuracy of the wall-shear stress estimates with synchronized wall-shear stress measurements using the Micro-Pillar Shear-Stress Sensor for Reynolds numbers up to 2,000. In summary, the presented framework lays the groundwork for extracting inaccessible experimental wall-shear stress information from readily available velocity measurements and thus, facilitates advancements in a variety of experimental applications.