Uncertainty quantification for generalized Langevin dynamics
Abstract
Here, we present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of the GLE where other well known sensitivity analysis techniques such as the likelihood ratio method are not applicable to key parameters of interest. These easily implemented estimators are formed by coupling the nominal and perturbed dynamics appearing in the finite difference through a common driving noise or common random path. After developing a general framework for variance reduction via coupling, we demonstrate the optimality of the common random path coupling in the sense that it produces a minimal variance surrogate for the difference estimator relative to sampling dynamics driven by independent paths. In order to build intuition for the common random path coupling, we evaluate the efficiency of the proposed estimators for a comprehensive set of examples of interest in particle dynamics. These reduced variance difference estimators are also a useful tool for performing global sensitivity analysis and for investigating non-local perturbations of parameters, such as increasing the number of Prony modes active in an extended variable GLE.
- Authors:
-
[1];
[1]
- Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics
- Publication Date:
- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1465368
- Alternate Identifier(s):
- OSTI ID: 1336482
- Grant/Contract Number:
- SC0010723; DMS-1515712
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 145; Journal Issue: 22; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Hall, Eric J., Katsoulakis, Markos A., and Rey-Bellet, Luc. Uncertainty quantification for generalized Langevin dynamics. United States: N. p., 2016.
Web. doi:10.1063/1.4971433.
Hall, Eric J., Katsoulakis, Markos A., & Rey-Bellet, Luc. Uncertainty quantification for generalized Langevin dynamics. United States. https://doi.org/10.1063/1.4971433
Hall, Eric J., Katsoulakis, Markos A., and Rey-Bellet, Luc. Wed .
"Uncertainty quantification for generalized Langevin dynamics". United States. https://doi.org/10.1063/1.4971433. https://www.osti.gov/servlets/purl/1465368.
@article{osti_1465368,
title = {Uncertainty quantification for generalized Langevin dynamics},
author = {Hall, Eric J. and Katsoulakis, Markos A. and Rey-Bellet, Luc},
abstractNote = {Here, we present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of the GLE where other well known sensitivity analysis techniques such as the likelihood ratio method are not applicable to key parameters of interest. These easily implemented estimators are formed by coupling the nominal and perturbed dynamics appearing in the finite difference through a common driving noise or common random path. After developing a general framework for variance reduction via coupling, we demonstrate the optimality of the common random path coupling in the sense that it produces a minimal variance surrogate for the difference estimator relative to sampling dynamics driven by independent paths. In order to build intuition for the common random path coupling, we evaluate the efficiency of the proposed estimators for a comprehensive set of examples of interest in particle dynamics. These reduced variance difference estimators are also a useful tool for performing global sensitivity analysis and for investigating non-local perturbations of parameters, such as increasing the number of Prony modes active in an extended variable GLE.},
doi = {10.1063/1.4971433},
journal = {Journal of Chemical Physics},
number = 22,
volume = 145,
place = {United States},
year = {Wed Dec 14 00:00:00 EST 2016},
month = {Wed Dec 14 00:00:00 EST 2016}
}
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