External potentials for bottom-up coarse-graining of inhomogeneous fluids: On improving thermodynamic transferability

Bottom-up coarse-grained models derived from all-atom simulations of interfacial or strongly inhomogeneous molecular fluids often suffer from limited thermodynamic transferability due to insufficient sampling of composition variations in the reference simulations, which can bias learned interactions. Rather than increasing model complexity, we show that simple, pairwise coarse-grained models can achieve improved thermodynamic transferability when trained on reference ensembles with enhanced thermodynamic information. We introduce an external ensemble methodology that employs pairwise external potentials to drive equilibrium compositional fluctuations in the all-atom reference simulations of a model inhomogeneous dodecane-water system, thereby enriching the thermodynamic information available for coarse-graining. We show that this information content can be systematically quantified and optimized using a particle fluctuation number metric directly computable in the reference ensemble that is related to the Fisher information. Coupling this approach with relative entropy minimization, we show that maximizing the compositional fluctuations according to this information metric yields substantially improved coarse-grained model predictions of the all-atom alkane-water transfer free energies. We compare different coarse-graining protocols and types of external Gaussian potentials to show that this improvement is consistently observed. Finally, we show that improved alkane-water transfer free energies enhance predictions of hydrophobically driven self-assembly behavior, with external-ensemble-derived coarse-grained models yielding an order-of-magnitude improvement in the predicted critical micelle concentration of sodium dodecyl sulfate relative to conventionally derived coarse-grained models.