Error bounds for dynamical spectral estimation

Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular simulations, its error properties remain poorly understood. Here...

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Bibliographic Details
Published in:arXiv.org 2020-09
Main Authors: Webber, Robert J, Thiede, Erik H, Dow, Douglas, Dinner, Aaron R, Weare, Jonathan
Format: Article
Language:English
Subjects:
Computer simulation
Eigenvalues
Eigenvectors
Error analysis
Lag time
Mathematical analysis
Spectra
Trajectory analysis
Online Access:Get full text
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Summary:Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular simulations, its error properties remain poorly understood. Here we analyze the error of a dynamical spectral estimation method called "the variational approach to conformational dynamics" (VAC). We bound the approximation error and estimation error for VAC estimates. Our analysis establishes VAC's convergence properties and suggests new strategies for tuning VAC to improve accuracy.
ISSN:2331-8422
DOI:10.48550/arxiv.2005.02248