Error bounds for dynamical spectral estimation
arXiv:2005.02248 · doi:10.1137/20M1335984
Abstract
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.
arXiv comment34 pages, 7 figures
References in corpus (10)
- A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
- Identification of slow molecular order parameters for Markov model construction
- VAMPnets: Deep learning of molecular kinetics
- Data-driven model reduction and transfer operator approximation
- Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets
- Variational Koopman models: slow collective variables and molecular kinetics from short off-equilibrium simulations
- Peptide Folding Kinetics from Replica Exchange Molecular Dynamics
- Galerkin Approximation of Dynamical Quantities using Trajectory Data
- Markov State Models from short non-Equilibrium Simulations - Analysis and Correction of Estimation Bias
- Integrated VAC: A robust strategy for identifying eigenfunctions of dynamical operators