  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 (Y. Lu, J. Lu, and J.
Nolen, arXiv:1905.09863, 2019) 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 a new 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.
