A Drag Model for Rough Surfaces Learned Using Feature Importance-Informed Symbolic Regression

Abstract Predicting the drag of rough surfaces presents a long-standing challenge in fluid dynamics. To address this, we propose a new drag model developed through a feature importance-informed symbolic regression method. Our method begins by identifying the key geometrical statistics governing the equivalent sandgrain roughness height, ks, via a quantitative feature importance analysis. Using 96 rough surface data samples, we then derive an analytical expression for ks within this reduced feature space using symbolic regression with appropriately prescribed expression templates. The proposed model outperforms empirical correlations, which are often limited to specific roughness types and arrangements, across diverse surfaces. It achieves a mean absolute relative error of 9.60% and a maximum of 30.79%, performance comparable to typical black-box models, while retaining the advantages of interpretability and portability. Furthermore, the model demonstrates extrapolation capability by accurately predicting results for 8 unseen datasets that lie outside the feature space of the training data. The relevant source code and results are available at following footnote link.2