We present a hierarchical, three-step methodology for predicting the linear viscoelastic properties of entangled polymer melts. First, atomistic trajectories accumulated in the course of long molecular dynamics simulations with moderately entangled polymer melts are self-consistently mapped onto the tube model to compute the segment survival probability function psi(s, t) for primitive paths. Extracted directly from the atomistic simulations, the computed psi(s, t) accounts for all possible dynamic mechanisms affecting chain motion in entangled polymers such as reptation, contour length fluctuation, and constraint release. In a second step, the simulation predictions for psi(s, t) are compared with modern versions of the tube model, such as the dual constraint model of Pattamaprom et al. and the Leygue et al. model; the comparison reveals ways through which the two models can be improved and parameterized on the basis of the direct molecular simulation data. The key parameters turn out to be the entanglement chain length N-e and the entanglement time tau(e), both of which can be reliably extracted from the simulations. In a third step, the modified versions of the two models are invoked to predict the linear viscoelastic properties of the polymer under study over a broad range of molecular weights. The power of the new methodology is illustrated here for the case of linear polyethylene (PE) and cis- and trans-1,4 polybutadiene (PB) melts for which atomistic molecular dynamics data have already been obtained recently. We present results from the new approach for the zero-shear-rate viscosity eta(o), and the storage G' and loss G" moduli of the three polymers as a function of their molecular weight (MW), and a direct comparison with experimentally measured rheological data. (C) 2013 Elsevier B.V. All rights reserved.