一种局部高斯过程方法,用于拟合势面,避免了对大矩阵进行反演的需要

IF 1.4 4区 物理与天体物理 Q4 PHYSICS, ATOMIC, MOLECULAR & CHEMICAL
Nuoyan Yang , Spencer Hill , Sergei Manzhos , Tucker Carrington
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引用次数: 2

摘要

为了计算振动谱,人们通常希望从一组从头算的Born-Oppenheimer势值开始,称为拟合点,然后插值或拟合以找到正交点或配点的势值。通常这样做一次以建立势能面(PES)。一旦知道了PES,就可以在配置空间的任何点对其进行评估。高斯过程(GP)经常被用来制作PES。与其他插值方法一样,要使用GP,必须存储和反转一个矩阵,其大小是拟合点的数量。矩阵有时足够大,可以引入近似来减少计算成本。我们证明了使用多个局部高斯过程拟合而不是一个全局拟合是可能的。尽管其他高斯函数在局部区域具有显著振幅的尾巴,但仅保留局部高斯函数和相关点的效果很好。我们证明,从从局部拟合获得的势能值,可以计算出准确的甲醛能级。在一次计算中,通过对小于m=400的矩阵进行反演,得到N=120,000个拟合点的势值。局部思想将代价从N3降低到T(m3+N),其中T是期望的潜在点的数量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A local Gaussian Processes method for fitting potential surfaces that obviates the need to invert large matrices

A local Gaussian Processes method for fitting potential surfaces that obviates the need to invert large matrices

In order to compute a vibrational spectrum, one often wishes to start with a set of ab initio Born–Oppenheimer potential values at points, called fitting points, and interpolate or fit to find values of the potential at quadrature or collocation points. It is common to do this once to build a potential energy surface (PES). Once the PES is known, it can be evaluated at any point in configuration space. Gaussian Process (GP) is frequently being used to make a PES. As is the case in other interpolation methods, to use GP one must store and invert a matrix whose size is the number of fitting points. The matrix is sometimes large enough that approximations are introduced to reduce the cost of the calculation. We show that is possible to use many local Gaussian Process fits rather than one global fit. Retaining only local Gaussians and the associated points works well despite the fact that other Gaussians have tails with significant amplitude in the local region. We demonstrate that from the potential values obtained from the local fits it is possible to compute accurate energy levels of formaldehyde. In one calculation, potential values were obtained with N=120,000 fitting points by inverting matrices of size less than m=400. The local idea reduces the cost from N3 to T(m3+N), where T is the number of desired potential points.

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来源期刊
CiteScore
2.70
自引率
21.40%
发文量
94
审稿时长
29 days
期刊介绍: The Journal of Molecular Spectroscopy presents experimental and theoretical articles on all subjects relevant to molecular spectroscopy and its modern applications. An international medium for the publication of some of the most significant research in the field, the Journal of Molecular Spectroscopy is an invaluable resource for astrophysicists, chemists, physicists, engineers, and others involved in molecular spectroscopy research and practice.
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