  Finding saddle points of dynamical systems is an important problem in
practical applications such as the study of rare events of molecular systems.
Gentlest ascent dynamics (GAD) is one of a number of algorithms in existence
that attempt to find saddle points in dynamical systems. It works by deriving a
new dynamical system in which saddle points of the original system become
stable equilibria. GAD has been recently generalized to the study of dynamical
systems on manifolds (differential algebraic equations) described by equality
constraints and given in an extrinsic formulation. In this paper, we present an
extension of GAD to manifolds defined by point-clouds, formulated using the
intrinsic viewpoint. These point-clouds are adaptively sampled during an
iterative process that drives the system from the initial conformation
(typically in the neighborhood of a stable equilibrium) to a saddle point. Our
method requires the reactant (initial conformation), does not require the
explicit constraint equations to be specified, and is purely data-driven.
