自适应采样点云定义流形上的最缓上升动力学
Gentlest ascent dynamics on manifolds defined by adaptively sampled point-clouds
AI总结：
本文将最缓上升动力学（GAD）扩展到由自适应采样点云定义的内蕴流形，无需显式约束方程即可从初始构象数据驱动地定位鞍点。
摘要：
寻找动力系统的鞍点是实际应用中的一个重要问题，例如研究分子系统的稀有事件。最缓上升动力学（GAD）是现有众多试图寻找动力系统鞍点的算法之一。它通过推导一个新的动力系统来工作，在该系统中，原系统的鞍点变为稳定平衡点。GAD最近已被推广到研究由等式约束描述、并以外蕴形式给出的流形上的动力系统（微分代数方程）。在本文中，我们将GAD扩展到由点云定义的流形，并采用内蕴视角进行表述。这些点云是在一个迭代过程中自适应采样的，该过程驱动系统从初始构象（通常位于稳定平衡点附近）到达鞍点。我们的方法只需要反应物（初始构象），不需要指定显式约束方程，并且是纯数据驱动的。
英文摘要：
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.
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