Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression
Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression
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DOI：
10.1063/1.4964902
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发表时间：
2016-11-07
影响因子：
4.4
通讯作者：
Habershon, Scott
中科院分区：
文献类型：
--
作者：
Alborzpour, Jonathan P.;Tew, David P.;Habershon, Scott
使用基函数的线性组合（例如高斯波包（GWP））求解时间相关薛定谔方程需要对系统的整个势能面（PES）上的积分进行昂贵的评估。标准的方法，由直接动力学的计算易处理性的动机，是近似PES与二阶泰勒展开，例如在每个GWP为中心。在这篇文章中，我们提出了一种替代的方法来近似PES矩阵元素的基础上PES插值高斯过程回归（GPR）。我们的GPR方案只需要单点评估的PES在有限数量的配置在每个时间步，执行通常昂贵的评估的Hessian矩阵的必要性是完全避免的。在应用到2-，5-，和10维的基准模型描述隧道坐标非线性耦合到一组谐振子，我们发现，我们的GPR方法的结果在PES矩阵元素的平均误差是，在最好的情况下，两个数量级小，在最坏的情况下，直接可比的任何其他泰勒展开法确定，而不需要额外的PES评估或Hessian矩阵。考虑到GPR的计算简单性，以及进一步完善本文所强调的程序的机会，我们认为，我们的GPR方法应该取代在量子动力学模拟中使用泰勒展开来评估PES矩阵元素的方法。(C)2016年作者。
Solution of the time-dependent Schrodinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each timestep; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. (C) 2016 Author(s).