Interpreting and Modeling Surface Roughness Effects via Drag-Augmented Manifold Learning

Surface roughness in turbulent wall-bounded flows increases drag, affecting fluid transport and hydrodynamic performance, and thus demands accurate prediction. Empirical correlations are inexpensive but valid only within limited roughness regimes, whereas neural networks improve accuracy at the expense of interpretability. An observable-augmented manifold learning framework is proposed to derive a low-order representation of roughness effects on turbulent drag. Using direct numerical simulation data at Re_τ=500, the model predicts the roughness function ΔU⁺ while simultaneously reconstructing the input surface. An autoencoder compresses height maps into latent vectors—reducing input dimensionality by up to 98%—achieving a mean absolute percentage error of 7.7% in ΔU⁺ and a mean reconstruction error of approximately 3.6 viscous units. Principal component analysis then projects the latent space onto a three-dimensional manifold, capturing the dominant physical mechanisms influencing drag. Finally, symbolic regression is applied to correlate this PCA–AE manifold with traditional roughness and turbulence metrics, enhancing interpretability and identifying key drag parameters. This low-dimensional, physics-informed representation balances accuracy and explainability, providing an efficient tool for analyzing complex fluid dynamics problems.