# Predicting the wall-shear stress and wall pressure through convolutional neural networks

arXiv: https://arxiv.org/abs/2303.00706 · HTML: https://mlsanity.com/paper/2303.00706/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Scientific multi-agent reinforcement learning for wall-models of turbulent flows](https://mlsanity.com/paper/2106.11144/) (2021)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Deep Neural Networks for Data-Driven Turbulence Models](https://mlsanity.com/paper/1806.04482/) (2018)
- [Predicting the temporal dynamics of turbulent channels through deep learning](https://mlsanity.com/paper/2203.00974/) (2022)

## Built on by (most cited first, 2 of 2)

- [Uncovering wall-shear stress dynamics from neural-network enhanced fluid flow measurements](https://mlsanity.com/paper/2310.11147/) (2023)
- [A deep learning approach to wall-shear stress quantification: From numerical training to zero-shot experimental application](https://mlsanity.com/paper/2409.03933/) (2024)

## Abstract (arXiv)

The objective of this study is to assess the capability of convolution-based neural networks to predict wall quantities in a turbulent open channel flow. The first tests are performed by training a fully-convolutional network (FCN) to predict the 2D velocity-fluctuation fields at the inner-scaled wall-normal location y+rm target, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at y+rm input. The predictions from the FCN are compared against the predictions from a proposed R-Net architecture. Since the R-Net model is found to perform better than the FCN model, the former architecture is optimized to predict the 2D streamwise and spanwise wall-shear-stress components and the wall pressure from the sampled velocity-fluctuation fields farther from the wall. The dataset is obtained from DNS of open channel flow at Reτ = 180 and 550. The turbulent velocity-fluctuation fields are sampled at various inner-scaled wall-normal locations, along with the wall-shear stress and the wall pressure. At Reτ=550, both FCN and R-Net can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at y+ = 50 using the velocity-fluctuation fields at y+ = 100 as input with about 10% error in prediction of streamwise-fluctuations intensity. Further, the R-Net is also able to predict the wall-shear-stress and wall-pressure fields using the velocity-fluctuation fields at y^+ = 50 with around 10% error in the intensity of the corresponding fluctuations at both Reτ = 180 and 550. These results are an encouraging starting point to develop neural-network-based approaches for modelling turbulence near the wall in large-eddy simulations.