(373g) Improving the Efficiency of Visited States Approaches to Expanded Ensemble Simulations

Expanded or generalized ensemble methods are a broad class of methods that can be used to overcome sampling difficulties by adding transitions between thermodynamic ensembles. They are similar to replica exchange methods, except that are performed with single simulations rather than a set of parallel simulations, which makes them much more suitable for many computing environments. These additional thermodynamic ensembles can either be ensembles of interest (for example, the same system at different temperatures if temperature dependent effects are of interest) or auxiliary states added to either improve overlap between end states or to improve sampling by introducing states with faster kinetics.

One weakness of these methods is that in order to sample states at all ensembles with reasonable frequency, simulation weights for each of the sub-ensembles must added. These weights must be determined self-consistently, and the choice of algorithm to determine these self-consistent algorithms can significantly affect the results.

We show how approaches such as Wang-Landau and Transition Matrix methods can be generalized when dealing with expanded ensemble systems containing many thermodynamic states. Specifically, we discuss how these can be seen as approximations to optimal multistate free energy estimators such as MBAR (the multistate Bennett's acceptance ratio method) and as the Rao-Blackwellization of the Wang-Landau estimator. This more general multistate approach allows more efficient determination of free energies and other observables over many states simultaneously, especially when the states are arranged in a multidimensional network, with multiple neighbors in each state.

We additionally show how these multistate estimation methods can be combined with Gibbs sampling techniques, a generalization of Metropolis Monte Carlo methods which includes transitions to all possible states. This combination allows efficient sampling and property prediction over hundreds or thousands of thermodynamic states. We look at applications of these combined methods to searching the parameter space of spatially dependent Ising models as well as as well computing the binding free energy of small molecules to simple molecular containers.