We study fluid permeability in random sphere packings consisting of impermeable monodisperse hard spheres. Several different pseudo-potential models are used to obtain varying degrees of microstructural heterogeneity. Systematically varying solid volume fraction and degree of heterogeneity, virtual screening of more than 10,000 material structures is performed, simulating fluid flow using a lattice Boltzmann framework and computing the permeability. We develop a well-performing functional regression model for permeability prediction based on using isotropic two-point correlation functions as microstructural descriptors. The performance is good over a large range of solid volume fractions and degrees of heterogeneity, and to our knowledge this is the first attempt at using two-point correlation functions as functional predictors in a nonparametric statistics/machine learning context for permeability prediction.