Drag prediction of rough-wall turbulent flow using data-driven regression

TL;DR

This study evaluates various data-driven regression models, including linear, kernel, and neural networks, for predicting drag in rough-wall turbulent flows, highlighting their capabilities and limitations based on a large surface database.

Contribution

The paper compares the performance of different regression techniques for drag prediction, emphasizing the effectiveness of kernel methods and neural networks with limited data.

Findings

Kernel methods accurately model nonlinear relations with few parameters

Linear regression shows large errors due to inability to capture nonlinearities

Neural networks require more data to fully utilize their capacity

Abstract

Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, methods for drag prediction rely on experiments or numerical simulations which are costly and time-consuming. Data-driven regression methods have the potential to provide a prediction that is accurate and fast. We assess the performance and limitations of linear regression, kernel methods and neural networks for drag prediction using a database of 1000 homogeneous rough surfaces. Model performance is evaluated using the roughness function obtained at friction-scaled Reynolds number 500. With two trainable parameters, the kernel method can fully account for nonlinear relations between $\Delta U^+$ and surface statistics (roughness height, effective slope, skewness, etc). In contrast, linear regression cannot account for nonlinear correlations and display large errors and high uncertainty. Multilayer perceptron and convolutional neural networks demonstrate performance on par with the kernel method but have orders of magnitude more trainable parameters. For the current database size, the networks' capacity cannot be fully exploited, resulting in reduced generalizability and reliability. Our study provides insight into the appropriateness of different regression models for drag prediction. We also discuss the remaining steps before data-driven methods emerge as useful tools in applications.