Learning Markovian dynamics with spectral maps

Jakub Rydzewski; Tuğçe Gökdemir

doi:10.1063/5.0189241

Learning Markovian dynamics with spectral maps

J Chem Phys. 2024 Mar 7;160(9):091102. doi: 10.1063/5.0189241.

Authors

Jakub Rydzewski¹, Tuğçe Gökdemir¹

Affiliation

¹ Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland.

PMID: 38436438
DOI: 10.1063/5.0189241

Abstract

The long-time behavior of many complex molecular systems can often be described by Markovian dynamics in a slow subspace spanned by a few reaction coordinates referred to as collective variables (CVs). However, determining CVs poses a fundamental challenge in chemical physics. Depending on intuition or trial and error to construct CVs can lead to non-Markovian dynamics with long memory effects, hindering analysis. To address this problem, we continue to develop a recently introduced deep-learning technique called spectral map [J. Rydzewski, J. Phys. Chem. Lett. 14, 5216-5220 (2023)]. Spectral map learns slow CVs by maximizing a spectral gap of a Markov transition matrix describing anisotropic diffusion. Here, to represent heterogeneous and multiscale free-energy landscapes with spectral map, we implement an adaptive algorithm to estimate transition probabilities. 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.