Optimizing the sampling and staging for simulations of rare events via forward flux sampling schemes

In this work, we present an adaptive algorithm to optimize the phase space sampling for simulations of rare events in complex systems via forward flux sampling (FFS) schemes. In FFS, interfaces are used to partition the phase space along an order parameter lambda connecting the initial and final regions of interest. Since the kinetic "bottleneck" regions along the order parameter are not usually known beforehand, an adaptive procedure is used that first finds these regions by estimating the rate constants associated with reaching subsequent interfaces; thereafter, the FFS simulation is reset to concentrate the sampling on those bottlenecks. The approach can optimize for either the number and position of the interfaces (i.e., optimized lambda phase staging) or the number M of fired trial runs per interface (i.e., the {M(i)} set) to minimize the statistical error in the rate constant estimation per simulation period. For example, the optimization of the lambda staging leads to a net constant flux of partial trajectories between interfaces and hence a constant flux of connected paths throughout the region between the two end states. The method is demonstrated for several test systems, including the folding of a lattice protein. It is shown that the proposed approach leads to an optimized lambda staging and {M(i)} set which increase the computational efficiency of the sampling algorithm.