  Understanding the influence of surface roughness on drag forces remains a
significant challenge in fluid dynamics. This paper presents a convolutional
neural network (CNN) that predicts drag solely by the topography of rough
surfaces and is capable of discovering spatial patterns linked to drag-inducing
structures. A CNN model was developed to analyze spatial information from the
topography of a rough surface and predict the roughness function, $\Delta U^+$,
obtained from direct numerical simulation. This model enables the prediction of
drag from rough surface data alone, which was not possible with previous
methods owing to the large number of surface-derived parameters. Additionally,
the retention of spatial information by the model enables the creation of a
feature map that accentuates critical areas for drag prediction on rough
surfaces. By interpreting the feature maps, we show that the developed CNN
model is able to discover spatial patterns associated with drag distributions
across rough surfaces, even without a direct training on drag distribution
data. The analysis of the feature map indicates that, even without flow field
information, the CNN model extracts the importance of the flow-directional
slope and height of roughness elements as key factors in inducing pressure
drag. This study demonstrates that CNN-based drag prediction is grounded in
physical principles of fluid dynamics, underscoring the utility of CNNs in both
predicting and understanding drag on rough surfaces.
