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Gentlest Ascent Dynamics on Manifolds Defined by Adaptively Sampled Point-Clouds

  • Juan M. Bello-Rivas*
    Juan M. Bello-Rivas
    Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, United States
    *E-mail: [email protected]
  • Anastasia Georgiou
    Anastasia Georgiou
    Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, United States
  • Hannes Vandecasteele
    Hannes Vandecasteele
    Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium
  • , and 
  • Ioannis G. Kevrekidis*
    Ioannis G. Kevrekidis
    Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, United States
    Departments of Applied Mathematics and Statistics, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, United States
    *E-mail: [email protected]
Cite this: J. Phys. Chem. B 2023, 127, 23, 5178–5189
Publication Date (Web):June 6, 2023
https://doi.org/10.1021/acs.jpcb.3c00897
Copyright © 2023 American Chemical Society

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    Abstract

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    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) (10.1088/0951-7715/24/6/008) is one of a number of algorithms in existence that attempt to find saddle points. 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 (10.1007/s10915-022-01838-3) and given in an extrinsic formulation. In this paper, we present an extension of GAD to manifolds defined by point-clouds, formulated by using an 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.

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