  A strategy is developed for generating equilibrated high molecular-weight
polymer melts described with microscopic detail by sequentially backmapping
coarse-grained (CG) configurations. The microscopic test model is generic but
retains features like hard excluded volume interactions and realistic melt
densities. The microscopic representation is mapped onto a model of soft
spheres with fluctuating size, where each sphere represents a microscopic
subchain with $N_{\rm b}$ monomers. By varying $N_{\rm b}$ a hierarchy of CG
representations at different resolutions is obtained. Within this hierarchy, CG
configurations equilibrated with Monte Carlo at low resolution are sequentially
fine-grained into CG melts described with higher resolution. A Molecular
Dynamics scheme is employed to slowly introduce the microscopic details into
the latter. All backmapping steps involve only local polymer relaxation thus
the computational efficiency of the scheme is independent of molecular weight,
being just proportional to system size. To demonstrate the robustness of the
approach, microscopic configurations containing up to $n=1000$ chains with
polymerization degrees $N=2000$ are generated and equilibration is confirmed by
monitoring key structural and conformational properties. The extension to much
longer chains or branched polymers is straightforward.
