Predicting the bulk cross-sectional average flow velocity in open channels with submerged vegetation is an important topic in river engineering. Researchers have proposed numerous theoretical and empirical formulae, but the accuracy and physical basis of their solutions still need improvement. This study separates the flow into vegetation layer and surface layer, following conventional two-layer approach, and estimates the average velocities in these two layers separately. In the vegetation layer, force balance equation provides the basement of the estimation. And in the surface layer, we use genetic programming (GP), a data-driven method. A Darcy-Weisbach-coefficient-like parameter is proposed for the surface layer, which is related to other parameters through the GP algorithm. The maximum dissimilarity algorithm (a data-clustering algorithm) is used to separate the existing data sets in the training, validation …