Sampling rare event energy landscapes via birth-death augmented dynamics

A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the presences of high kinetic barriers that hinder transitions between metastable states on typical simulation time scales. Many enhanced sampling methods have been developed to address this sampling problem and more efficiently sample rare event systems. An interesting idea, coming from the field of statistics, was introduced in a recent work [Lu, Lu, and Nolen, Accelerating Langevin sampling with birth-death, arXiv:1905.09863] in the form of a novel sampling algorithm that augments overdamped Langevin dynamics with a birth-death process. In this work, we expand on this idea and show that this birth-death sampling scheme can efficiently sample prototypical rare event energy landscapes, and that the speed of equilibration is independent of the barrier height. We amend a crucial shortcoming of the original algorithm that leads to incorrect sampling of barrier regions by introducing an alternative approximation of the birth-death term. We establish important theoretical properties of the modified algorithm and prove mathematically that the relevant convergence results still hold. We investigate via numerical simulations the effect of various parameters, and we investigate ways to reduce the computational effort of the sampling scheme. We show that the birth-death mechanism can be used to accelerate sampling in the more general case of underdamped Langevin dynamics that is more commonly used in simulating physical systems. Our results show that this birth-death scheme is a promising method for sampling rare event energy landscapes.