Gentlest ascent dynamics on manifolds defined by adaptively sampled point-clouds
This work addresses the challenge of studying rare events in molecular systems for researchers in computational chemistry and physics, representing an incremental extension of existing GAD methods.
The paper tackles the problem of finding saddle points in dynamical systems on manifolds defined by point-clouds, presenting an extension of Gentlest Ascent Dynamics (GAD) that uses adaptive sampling and an intrinsic formulation, achieving a data-driven approach without explicit constraint equations.
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.