Galerkin approximation of dynamical quantities using trajectory data

Erik H. Thiede, Dimitrios Giannakis, Aaron R. Dinner, Jonathan Weare

Research output: Contribution to journalArticle

Abstract

Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion. A specific choice of basis set in the expansion corresponds to the estimation of dynamical quantities using a Markov state model. More generally, the boundary conditions impose restrictions on the choice of basis sets. We demonstrate how an alternative basis can be constructed using ideas from diffusion maps. In our numerical experiments, this basis gives results of comparable or better accuracy to Markov state models. Additionally, we show that delay embedding can reduce the information lost when projecting the system's dynamics for model construction; this improves estimates of dynamical statistics considerably over the standard practice of increasing the lag time.

Original languageEnglish (US)
Article number244111
JournalJournal of Chemical Physics
Volume150
Issue number24
DOIs
StatePublished - Jun 28 2019

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Trajectories
trajectories
approximation
Statistics
statistics
expansion
boundary value problems
embedding
Boundary value problems
Reaction rates
Mathematical operators
constrictions
Dynamical systems
reaction kinetics
estimating
time lag
Boundary conditions
boundary conditions
operators
estimates

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Galerkin approximation of dynamical quantities using trajectory data. / Thiede, Erik H.; Giannakis, Dimitrios; Dinner, Aaron R.; Weare, Jonathan.

In: Journal of Chemical Physics, Vol. 150, No. 24, 244111, 28.06.2019.

Research output: Contribution to journalArticle

Thiede, Erik H. ; Giannakis, Dimitrios ; Dinner, Aaron R. ; Weare, Jonathan. / Galerkin approximation of dynamical quantities using trajectory data. In: Journal of Chemical Physics. 2019 ; Vol. 150, No. 24.
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