Institut für Theoretische Physik 1 , Universität Stuttgart , 70550 Stuttgart , Germany.
Centre for Nonlinear Mathematics and Applications, Department of Mathematical Sciences , Loughborough University , Loughborough LE11 3TU , United Kingdom.
J Phys Chem B. 2019 Mar 7;123(9):2070-2086. doi: 10.1021/acs.jpcb.8b10541. Epub 2019 Feb 20.
Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets and introduce the use of Gaussian process regression for the determination of the NHIM. Finally, we compare and contrast all of these methods for a challenging two-dimensional model barrier case so as to illustrate their accuracy and general applicability.
在非平衡条件下，化学反应的反应速率可以通过构建与过渡态轨迹相关的通常双曲不变流形（NHIM）[和移动分界面（DS）]来确定。在这里，我们通过构建 NHIM 上的点来扩展我们最近的方法，即使对于多维情况也是如此，这些点的构建非常精确。我们还推进了机器学习方法的实施，以便从 NHIM 的已知高精度点集构建其平滑版本。也就是说，我们扩展了我们早期使用神经网络的方法，并引入了使用高斯过程回归来确定 NHIM。最后，我们对所有这些方法进行了比较和对比，以说明它们的准确性和普遍适用性，使用了一个具有挑战性的二维模型势垒案例。
