  Stochastic systems often exhibit multiple viable metastable states that are
long-lived. Over very long timescales, fluctuations may push the system to
transition between them, drastically changing its macroscopic configuration. In
realistic systems, these transitions can happen via multiple physical
mechanisms, corresponding to multiple distinct transition channels for a pair
of states. In this paper, we use the fact that the transition path ensemble is
equivalent to the invariant measure of a gradient flow in pathspace, which can
be efficiently sampled via metadynamics. We demonstrate how this pathspace
metadynamics, previously restricted to reversible molecular dynamics, is in
fact very generally applicable to metastable stochastic systems, including
irreversible and time-dependent ones, and allows to estimate rigorously the
relative probability of competing transition paths. We showcase this approach
on the study of a stochastic partial differential equation describing magnetic
field reversal in the presence of advection.
