  A hallmark of meso-scale interfacial fluids is the multi-faceted,
scale-dependent interfacial energy, which often manifests different
characteristics across the molecular and continuum scale. The multi-scale
nature imposes a challenge to construct reliable coarse-grained (CG) models,
where the CG potential function needs to faithfully encode the many-body
interactions arising from the unresolved atomistic interactions and account for
the heterogeneous density distributions across the interface. We construct the
CG models of both single- and two-component of polymeric fluid systems based on
the recently developed deep coarse-grained potential (DeePCG) scheme, where
each polymer molecule is modeled as a CG particle. By only using the training
samples of the instantaneous force under the thermal equilibrium state, the
constructed CG models can accurately reproduce both the probability density
function of the void formation in bulk and the spectrum of the capillary wave
across the fluid interface. More importantly, the CG models accurately predict
the volume-to-area scaling transition for the apolar solvation energy,
illustrating the effectiveness to probe the meso-scale collective behaviors
encoded with molecular-level fidelity.
