# (113e) Multiscale Optimization of Coarse-Grained Models Via the Relative Entropy

- Conference: AIChE Annual Meeting
- Year: 2009
- Proceeding: 2009 AIChE Annual Meeting
- Group: Computational Molecular Science and Engineering Forum
- Session:
- Time:
Monday, November 9, 2009 - 1:50pm-2:10pm

Multiscale simulation methods are commonly used to study the properties of complex systems with multiple length and time scales [1]. These methods often connect detailed all-atom (AA) molecular models with simplified coarse-grained (CG) ones that enable longer and larger simulation studies. However, it has been challenging to identify optimal yet universal parameterization methodologies for the development of CG models. Recently, we introduced a rigorous theoretical framework for such a task: given an AA model, an optimal CG one can be determined by minimizing an informatic property termed the relative entropy [2]. In physical terms, the relative entropy measures deviations in the configurational ensemble probabilities as molecular features are coarse-grained away. In a previous work, it was shown that the relative entropy method naturally reproduces important inverse problems in statistical mechanics, including uniqueness theorem and variational mean field theory [2].

In this work, we present two methods for numerical optimization of CG models using relative entropy minimization. One is based on the original formulation of the relative entropy, and it involves computing property averages via simulations in both the AA and CG ensembles. Using standard free energy perturbation techniques, we present an alternative approach that requires only averages in the AA ensemble, allowing for a very fast implementation; furthermore, this reformulation of the relative entropy permits a basic expansion which yields analytical expressions for optimization in special cases. We first compare the statistical efficiency and convergence behavior of these approaches via an elementary test case, the ?coarse-graining? of the nearest-neighbor lattice gas into the comparable mean-field system. We demonstrate that our mean-field solution performs in a superior manner with respect to the traditional mean-field approach. Moreover, we show that the relative entropy systematically signals the performance of the mean-field systems, thus serving as an apparent universal metric for the aptitude of CG models. Subsequently, we use the relative entropy approach to parameterize a simple (off-lattice) spherically-symmetric model of liquid water [3]. We evaluate the ability of the optimized CG water in reproducing water's bulk thermophysical properties and the hydrophobic effect [3]. Again, we show that the relative entropy serves as an indicator of the capability of these optimized models.

1. Voth, G.A., Introduction: Coarse-Graining in Molecular Modeling and Simulation. Journal of Chemical Theory and Computation, 2006. 2(3): p. 463-463.

2. Shell, M.S., The relative entropy is fundamental to multiscale and inverse thermodynamic problems. The Journal of Chemical Physics, 2008. 129(14): p. 144108-7.

3. Chaimovich, A. and M.S. Shell, Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy. Physical Chemistry Chemical Physics, 2009. 11(12): p. 1901-1915.