Prediction of wall-bounded turbulence from wall quantities using convolutional neural networks

TL;DR

This paper demonstrates that convolutional neural networks can accurately predict wall-bounded turbulence flow fields from wall measurements, outperforming linear methods and enabling efficient, generalizable turbulence predictions.

Contribution

It introduces a CNN-based approach for turbulence prediction from wall data, showing improved accuracy, transfer learning benefits, and insights into network design for turbulence modeling.

Findings

CNN outperforms linear methods in turbulence prediction.

Higher sampling intervals improve model generalization.

Transfer learning reduces training time by a factor of 4.

Abstract

A fully-convolutional neural-network model is used to predict the streamwise velocity fields at several wall-normal locations by taking as input the streamwise and spanwise wall-shear-stress planes in a turbulent open channel flow. The training data are generated by performing a direct numerical simulation (DNS) at a friction Reynolds number of $Re_{\tau}=180$. Various networks are trained for predictions at three inner-scaled locations ($y^+ = 15,~30,~50$) and for different time steps between input samples $\Delta t^{+}_{s}$. The inherent non-linearity of the neural-network model enables a better prediction capability than linear methods, with a lower error in both the instantaneous flow fields and turbulent statistics. Using a dataset with higher $\Delta t^+_{s}$ improves the generalization at all the considered wall-normal locations, as long as the network capacity is sufficient to generalize over the dataset. The use of a multiple-output network, with parallel dedicated branches for two wall-normal locations, does not provide any improvement over two separated single-output networks, other than a moderate saving in training time. Training time can be effectively reduced, by a factor of 4, via a transfer learning method that initializes the network parameters using the optimized parameters of a previously-trained network.