  We apply a numerical minimum action method derived from the Wentzell-Freidlin
theory of large deviations to the Kardar-Parisi-Zhang equation for a growing
interface. In one dimension we find that the switching scenario is determined
by the nucleation and subsequent propagation of facets or steps, corresponding
to moving domain walls or growth modes in the underlying noise driven Burgers
equation. The transition scenario is in accordance with recent analytical
studies of the one dimensional Kardar-Parisi-Zhang equation in the asymptotic
weak noise limit. We also briefly discuss transitions in two dimensions.
