  We develop a non-empirical scheme to search for the minimum-energy escape
paths from the minima of the potential surface to unknown saddle points nearby.
A stochastic algorithm is constructed to move the walkers up the surface
through the potential valleys. This method employs only the local gradient and
diagonal part of the Hessian matrix of the potential. An application to a
two-dimensional model potential is presented to demonstrate the successful
finding of the paths to the saddle points. The present scheme could serve as a
starting point toward first-principles simulation of rare events across the
potential basins free from empirical collective variables.
