Datadriven parameterization of the generalized Langevin equation
Here, we present a datadriven 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 coarsegrain 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 fluctuationdissipation theorem is exactly satisfied.
 Authors:

^{[1]};
^{[1]};
^{[2]}
 Brown Univ., Providence, RI (United States)
 The Pennsylvania State Univ., University Park, PA (United States)
 Publication Date:
 Report Number(s):
 PNNLSA118385
Journal ID: ISSN 00278424; KJ0401000
 Grant/Contract Number:
 AC0576RL01830; 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 00278424
 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; fluctuationdissipation theorem; generalized langevin equation; generalized Langevin dynamics; datadriven parameterization; coarsegrained molecular models; reaction rate; model reduction
 OSTI Identifier:
 1333885
 Alternate Identifier(s):
 OSTI ID: 1339841
Lei, Huan, Baker, Nathan A., and Li, Xiantao. Datadriven parameterization of the generalized Langevin equation. United States: N. p.,
Web. doi:10.1073/pnas.1609587113.
Lei, Huan, Baker, Nathan A., & Li, Xiantao. Datadriven parameterization of the generalized Langevin equation. United States. doi:10.1073/pnas.1609587113.
Lei, Huan, Baker, Nathan A., and Li, Xiantao. 2016.
"Datadriven parameterization of the generalized Langevin equation". United States.
doi:10.1073/pnas.1609587113.
@article{osti_1333885,
title = {Datadriven parameterization of the generalized Langevin equation},
author = {Lei, Huan and Baker, Nathan A. and Li, Xiantao},
abstractNote = {Here, we present a datadriven 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 coarsegrain 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 fluctuationdissipation 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}
}