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Spectral Map: Embedding Slow Kinetics in Collective Variables
journal contributionposted on 2023-06-01, 11:03 authored by Jakub Rydzewski
The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a fundamental problem in physical chemistry. This problem is even more pronounced when CVs need to provide information about slow kinetics related to rare transitions between long-lived metastable states. To address this issue, we propose an unsupervised deep-learning method called spectral map. Our method constructs slow CVs by maximizing the spectral gap between slow and fast eigenvalues of a transition matrix estimated by an anisotropic diffusion kernel. We demonstrate our method in several high-dimensional reversible folding processes.
transition matrix estimatedlived metastable statesanisotropic diffusion kernelslow kinetics relatedembedding slow kineticsunsupervised deepspectral mapspectral gapseveral highrequire highrare transitionsprovide informationphysical systemsphysical chemistrymeaningful degreesidentifying cvsfast eigenvaluesdimensional representationcvs needcvs ).collective variables