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Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations
Hao Wu1, Feliks Nüske1, Fabian Paul1
1Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany.
The Journal of Chemical Physics
|April 24, 2017
Summary
This study extends variational approaches to molecular kinetics (VAC) and time-lagged independent component analysis (TICA) for non-equilibrium data. New Koopman models enable accurate kinetic analysis from short simulations without clustering.
Area of Science:
- Computational Chemistry
- Molecular Dynamics
- Chemical Kinetics
Background:
- Markov state models (MSMs) and master equation models approximate molecular kinetics using state space discretization.
- Variational approaches like VAC and TICA generalize MSMs, approximating kinetics with smooth basis functions.
- Estimating TICA/VAC from non-equilibrium data has been challenging, leading to biased results.
Purpose of the Study:
- To extend variational approaches (VAC, TICA) for analyzing molecular kinetics from non-equilibrium simulation data.
- To develop a method for constructing variationally optimal models from short, potentially non-equilibrium trajectories.
- To enable accurate estimation of molecular kinetics and metastable states without relying on clustering.
Main Methods:
- Utilizing Koopman operator theory and dynamic mode decomposition to generalize VAC and TICA.
- Developing a 'Koopman model' (coefficient matrix) that approximates the Koopman operator.
- Employing the Koopman model to reweight data to equilibrium and construct optimal models.
Main Results:
- The Koopman model allows for the computation of a stationary vector to reweight non-equilibrium data to equilibrium.
- Equilibrium expectation values and optimal reversible Koopman models can be constructed from short simulations.
- Eigenvalue decomposition of the Koopman model provides relaxation time scales and slow collective variables.
Conclusions:
- Koopman models generalize MSMs, TICA, and linear VAC, offering a powerful framework for molecular kinetics.
- This approach enables accurate kinetic analysis from non-equilibrium data and short simulations.
- Molecular kinetics can be described effectively without the need for cluster discretization.
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