Eigenvector method for umbrella sampling enables error analysis

Erik H. Thiede, Brian Van Koten, Jonathan Weare, Aaron R. Dinner

Research output: Contribution to journalArticle

Abstract

Umbrella sampling efficiently yields equilibrium averages that depend on exploring rare states of a model by biasing simulations to windows of coordinate values and then combining the resulting data with physical weighting. Here, we introduce a mathematical framework that casts the step of combining the data as an eigenproblem. The advantage to this approach is that it facilitates error analysis. We discuss how the error scales with the number of windows. Then, we derive a central limit theorem for averages that are obtained from umbrella sampling. The central limit theorem suggests an estimator of the error contributions from individual windows, and we develop a simple and computationally inexpensive procedure for implementing it. We demonstrate this estimator for simulations of the alanine dipeptide and show that it emphasizes low free energy pathways between stable states in comparison to existing approaches for assessing error contributions. Our work suggests the possibility of using the estimator and, more generally, the eigenvector method for umbrella sampling to guide adaptation of the simulation parameters to accelerate convergence.

Original languageEnglish (US)
Article number084115
JournalJournal of Chemical Physics
Volume145
Issue number8
DOIs
StatePublished - Aug 28 2016

Fingerprint

error analysis
Eigenvalues and eigenfunctions
estimators
Error analysis
eigenvectors
sampling
Sampling
theorems
simulation
Dipeptides
alanine
Alanine
Free energy
casts
free energy

ASJC Scopus subject areas

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

Cite this

Thiede, E. H., Van Koten, B., Weare, J., & Dinner, A. R. (2016). Eigenvector method for umbrella sampling enables error analysis. Journal of Chemical Physics, 145(8), [084115]. https://doi.org/10.1063/1.4960649

Eigenvector method for umbrella sampling enables error analysis. / Thiede, Erik H.; Van Koten, Brian; Weare, Jonathan; Dinner, Aaron R.

In: Journal of Chemical Physics, Vol. 145, No. 8, 084115, 28.08.2016.

Research output: Contribution to journalArticle

Thiede, EH, Van Koten, B, Weare, J & Dinner, AR 2016, 'Eigenvector method for umbrella sampling enables error analysis', Journal of Chemical Physics, vol. 145, no. 8, 084115. https://doi.org/10.1063/1.4960649
Thiede, Erik H. ; Van Koten, Brian ; Weare, Jonathan ; Dinner, Aaron R. / Eigenvector method for umbrella sampling enables error analysis. In: Journal of Chemical Physics. 2016 ; Vol. 145, No. 8.
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