Multi-channel, nonlinear predictions of core temperature and density profiles are performed for the SPARC tokamak (Creely et al 2020 J. Plasma Phys.86 865860502) accounting for both kinetic neoclassical and fully nonlinear gyro-kinetic turbulent fluxes. A series of flux-tube, nonlinear, electromagnetic simulations using the CGYRO code (Candy et al 2016 J. Comput. Phys.324 73–93) with six gyrokinetic species are coupled to a nonlinear optimizer using Gaussian process regression techniques. The simultaneous evolution of energy sources, including alpha heat, radiation, and energy exchange, coupled with these high fidelity models and techniques, leads to a converged solution in electron temperature, ion temperature and electron density channels with a minimal number of expensive gyrokinetic simulations without compromising accuracy.