Computing committors in collective variables via Mahalanobis diffusion maps
Computing committors in collective variables via Mahalanobis diffusion maps
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DOI：
10.1016/j.acha.2023.01.001
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发表时间：
2023-01-13
影响因子：
2.5
通讯作者：
Tiwary, Pratyush
中科院分区：
文献类型：
--
作者：
Evans, Luke;Cameron, Maria K.;Tiwary, Pratyush
分子和原子体系中的稀有事件，如共形变化和团簇重排的研究一直是化学物理中最重要的研究课题之一。关键的挑战是与长时间的等待时间，使分子模拟效率低下，高维阻碍使用偏微分方程为基础的方法，和过渡过程的复杂性或广度限制渐近方法的预测能力。扩散图是有前途的算法，以避免或减轻所有这些问题。我们采用Singer和Coifman（2008）提出的具有Mahalanobis核的扩散映射来描述集体变量中的分子动力学，其中扩散矩阵是位置依赖的，并且与Singer和Coifman考虑的情况不同，不与非同构相关联。我们提供了一个初步的证明，表明可以近似的生成器为这个ESTA离散到一个点云通过Mahalanobis扩散映射。我们用它来计算两个基准系统的集体变量中的提交函数：丙氨酸二肽和2D中的Lennard-Jones-7。为了验证我们的提交人的结果，我们比较我们的提交人功能的有限差分解决方案，或进行“提交人分析”所使用的分子动力学从业者。我们将Mahalanobis扩散图的输出与具有各向同性核的标准扩散图的输出进行对比，并表明前者比后者对提交者的估计更准确。(c)2023爱思唯尔公司All rights reserved.
The study of rare events in molecular and atomic systems such as conformal changes and cluster rearrangements has been one of the most important research themes in chemical physics. Key challenges are associated with long waiting times rendering molecular simulations inefficient, high dimensionality impeding the use of PDE-based approaches, and the complexity or breadth of transition processes limiting the predictive power of asymptotic methods. Diffusion maps are promising algorithms to avoid or mitigate all these issues. We adapt the diffusion map with Mahalanobis kernel proposed by Singer and Coifman (2008) for the SDE describing molecular dynamics in collective variables in which the diffusion matrix is position-dependent and, unlike the case considered by Singer and Coifman, is not associated with a diffeomorphism. We offer an elementary proof showing that one can approximate the generator for this SDE discretized to a point cloud via the Mahalanobis diffusion map. We use it to calculate the committor functions in collective variables for two benchmark systems: alanine dipeptide, and Lennard-Jones-7 in 2D. For validating our committor results, we compare our committor functions to the finite-difference solution or by conducting a "committor analysis" as used by molecular dynamics practitioners. We contrast the outputs of the Mahalanobis diffusion map with those of the standard diffusion map with isotropic kernel and show that the former gives significantly more accurate estimates for the committors than the latter. (c) 2023 Elsevier Inc. All rights reserved.