Modeling dust coagulation is essential for simulations of the early stages of planet formation. The sizes and distribution of the dust grains determine the optical depth and opacities, thus, linking the dust coagulation and transport processes to continuum observations of protoplanetary disks. The grain size evolution sets the initial conditions for planetesimal formation and the formation of entire planetary systems. Here, we present two new approaches for simplified models of dust coagulation that can be used as subgrid models in vertically integrated (2D) hydrodynamic simulations of protoplanetary disks. Both models work within a two-population prescription, where the dust size distribution is approximated by a truncated power law. Dust evolution is simulated using either semi-analytic expressions for growth and fragmentation (model 1, called 2pop) or a neural network that predicts the time evolution (model 2, called 2popML). We show that both models are in good agreement with local and global full dust coagulation simulations (DustPy), at a substantially faster runtime. This makes it possible to use them in two-dimensional hydrodynamic simulations.