Learning Composition-Transferable Coarse-Grained Models: Designing External Potential Ensembles to Maximize Thermodynamic Information*

Simulation of complex, heterogeneous molecular systems requires models that are thermodynamically accurate and transferable across composition. However, current bottom-up strategies for parametrizing coarse-grained (CG) models from all-atom simulations often poorly reproduce thermodynamic properties. Current remedies have largely focused on increasing the complexity of coarse-grained Hamiltonians and interaction potentials. Here, we pursue an orthogonal approach that instead seeks to design better coarse-graining ensembles, i.e., the state conditions under which bottom-up coarse graining is performed. We introduce a quantitative metric for the quality (or informativeness) of a given ensemble, based on the Fisher information metric. Moreover, we highlight a physical basis for the Fisher information in terms of variances of important structural variables. Using these ideas, we use the Fisher information to optimize externally applied potentials to improve sampling of composition fluctuations and variations. With this approach, we show that even very simple coarse-grained interaction potentials can be optimized to quantitatively reproduce activity coefficients of a methanol-water binary mixture across the entire composition range.