The ability to accurately represent polymer melts at various levels of coarse graining is of great interest because of the wide range of time and length scales over which relevant process take place. Schemes for developing effective interaction potentials for coarse-grained representations that incorporate microscopic level system information are generally numerical and thus suffer from issues of transferability because they are state dependent and must be recalculated for different system and thermodynamic parameters. Numerically derived potentials are also known to suffer from representability problems, in that they may preserve structural correlations in the coarse-grained representation but many often fail to preserve thermodynamic averages of the coarse-grained representation.!
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