Learning Markovian Dynamics with Spectral Maps
arXiv:2311.16411 · doi:10.1063/5.0189241
Abstract
The long-time behavior of many complex molecular systems is often governed by slow relaxation dynamics that can be described by a few reaction coordinates referred to as collective variables (CVs). However, identifying CVs hidden in a high-dimensional configuration space poses a fundamental challenge in chemical physics. To address this problem, we expand on a recently introduced deep-learning technique called spectral map [Rydzewski, J. Phys. Chem. Lett. 2023, 14, 22, 5216-5220]. Spectral map learns CVs by maximizing a spectral gap between slow and fast eigenvalues of a Markov transition matrix describing anisotropic diffusion. An introduced modification in the learning algorithm allows spectral map to represent multiscale free-energy landscapes. Through a Markov state model analysis, we validate that spectral map learns slow CVs related to the dominant relaxation timescales and discerns between long-lived metastable states.
Accepted version
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