  Importance sampling of trajectories has proved a uniquely successful strategy
for exploring rare dynamical behaviors of complex systems in an unbiased way.
Carrying out this sampling, however, requires an ability to propose changes to
dynamical pathways that are substantial, yet sufficiently modest to obtain
reasonable acceptance rates. Satisfying this requirement becomes very
challenging in the case of long trajectories, due to the characteristic
divergences of chaotic dynamics. Here we examine schemes for addressing this
problem, which engineer correlation between a trial trajectory and its
reference path, for instance using artificial forces. Our analysis is
facilitated by a modern perspective on Markov Chain Monte Carlo sampling,
inspired by non-equilibrium statistical mechanics, which clarifies the types of
sampling strategies that can scale to long trajectories. Viewed in this light,
the most promising such strategy guides a trial trajectory by manipulating the
sequence of random numbers that advance its stochastic time evolution, as done
in a handful of existing methods. In cases where this "noise guidance"
synchronizes trajectories effectively, as the Glauber dynamics of a
two-dimensional Ising model, we show that efficient path sampling can be
achieved even for very long trajectories.
