  We introduce a new stochastic algorithm to locate the index-1 saddle points
of a function $V:\mathbb R^d \to \mathbb R$, with $d$ possibly large. This
algorithm can be seen as an equivalent of the stochastic gradient descent which
is a natural stochastic process to locate local minima. It relies on two
ingredients: (i) the concentration properties on index-1 saddle points of the
first eigenmodes of the Witten Laplacian (associated with $V$) on $1$-forms and
(ii) a probabilistic representation of a partial differential equation
involving this differential operator. Numerical examples on simple molecular
systems illustrate the efficacy of the proposed approach.
