  Forward flux sampling (FFS) provides a convenient and efficient way to
simulate rare events in equilibrium or non-equilibrium systems. FFS ratchets
the system from an initial state to a final state via a series of interfaces in
phase space. The efficiency of FFS depends sensitively on the positions of the
interfaces. We present two alternative methods for placing interfaces
automatically and adaptively in their optimal locations, on-the-fly as an FFS
simulation progresses, without prior knowledge or user intervention. These
methods allow the FFS simulation to advance efficiently through bottlenecks in
phase space by placing more interfaces where the probability of advancement is
lower. The methods are demonstrated both for a single-particle test problem and
for the crystallization of Yukawa particles. By removing the need for manual
interface placement, our methods both facilitate the setting up of FFS
simulations and improve their performance, especially for rare events which
involve complex trajectories through phase space, with many bottlenecks.
