Evidence of information limitations in coarse-grained models

Developing accurate coarse-grained (CG) models is critical for addressing long time and length scale phenomena with molecular simulations. Here, we distinguish and quantify two sources of error that are relevant to CG models in order to guide further methods development: "representability" errors, which result from the finite basis associated with the chosen functional form of the CG model and mapping operator, and "information" errors, which result from the limited kind and quantity of data supplied to the CG parameterization algorithm. We have performed a systematic investigation of these errors by generating all possible CG models of three liquids (butane, 1-butanol, and 1,3-propanediol) that conserve a set of chemically motivated locality and topology relationships. In turn, standard algorithms (iterative Boltzmann inversion, IBI, and multiscale coarse-graining, MSCG) were used to parameterize the models and the CG predictions were compared with atomistic results. For off-target properties, we observe a strong correlation between the accuracy and the resolution of the CG model, which suggests that the approximations represented by MSCG and IBI deteriorate with decreasing resolution. Conversely, on-target properties exhibit an extremely weak resolution dependence that suggests a limited role of representability errors in model accuracy. Taken together, these results suggest that simple CG models are capable of utilizing more information than is provided by standard parameterization algorithms, and that model accuracy can be improved by algorithm development rather than resorting to more complicated CG models.