The depth-averaged velocity is the commonly used engineering quantity in natural rivers, and it needs to be predicted in advance, especially in flood seasons. A model that can provide a unified physical foundation for open channel flows with different canopy densities remains lacking despite ongoing researches. Here, we use the concept of the auxiliary bed to describe the influence of momentum exchange on rigid canopy elements with varying density and submergence. The auxiliary bed divides the vegetated flow into a basal layer and a suspension layer to predict average velocity in each layer separately. In the basal layer, the velocity profile is assumed to be uniform. In the suspension layer, a parameter called “penetration depth” is applied to present the variations in velocity distribution. We also apply a data-driven method, called genetic programming (GP), to derive Chezy-like predictors for average velocity …