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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 polymeric fluid systems based on the recently developed deep coarse-grained potential [Zhang et al., J. Chem. Phys. 149, 034101 (2018)] 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. 

We have developed an accurate and efficient deep-learning potential (DP) for graphane, which is a fully hydrogenated version of graphene, using a very small training set consisting of 1000 snapshots from a 0.5 ps density functional theory (DFT) molecular dynamics simulation at 1000 K. We have assessed the ability of the DP to extrapolate to system sizes, temperatures, and lattice strains not included in the training set. The DP performs surprisingly well, outperforming an empirical many-body potential when compared with DFT data for the phonon density of states, thermodynamic properties, velocity autocorrelation function, and stress–strain curve up to the yield point. This indicates that our DP can reliably extrapolate beyond the limit of the training data. We have computed the thermal fluctuations as a function of system size for graphane. We found that graphane has larger thermal fluctuations compared with graphene, but having about the same out-of-plane stiffness.