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Title: Data-driven parameterization of the generalized Langevin equation

Here, we present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.
Authors:
 [1] ;  [1] ;  [2]
  1. Brown Univ., Providence, RI (United States)
  2. The Pennsylvania State Univ., University Park, PA (United States)
Publication Date:
Report Number(s):
PNNL-SA-118385
Journal ID: ISSN 0027-8424; KJ0401000
Grant/Contract Number:
AC05-76RL01830; CM4
Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 113; Journal Issue: 50; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences, Washington, DC (United States)
Research Org:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; fluctuation-dissipation theorem; generalized langevin equation; generalized Langevin dynamics; data-driven parameterization; coarse-grained molecular models; reaction rate; model reduction
OSTI Identifier:
1333885
Alternate Identifier(s):
OSTI ID: 1339841

Lei, Huan, Baker, Nathan A., and Li, Xiantao. Data-driven parameterization of the generalized Langevin equation. United States: N. p., Web. doi:10.1073/pnas.1609587113.
Lei, Huan, Baker, Nathan A., & Li, Xiantao. Data-driven parameterization of the generalized Langevin equation. United States. doi:10.1073/pnas.1609587113.
Lei, Huan, Baker, Nathan A., and Li, Xiantao. 2016. "Data-driven parameterization of the generalized Langevin equation". United States. doi:10.1073/pnas.1609587113.
@article{osti_1333885,
title = {Data-driven parameterization of the generalized Langevin equation},
author = {Lei, Huan and Baker, Nathan A. and Li, Xiantao},
abstractNote = {Here, we present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.},
doi = {10.1073/pnas.1609587113},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 50,
volume = 113,
place = {United States},
year = {2016},
month = {11}
}