Data-driven parameterization of the generalized Langevin equation

Lei, Huan; Baker, Nathan A.; Li, Xiantao

doi:10.1073/pnas.1609587113

Title: Data-driven parameterization of the generalized Langevin equation

Journal Article · Tue Nov 29 00:00:00 EST 2016 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.1609587113· OSTI ID:1333885

Lei, Huan ^[1]; Baker, Nathan A. ^[2]; Li, Xiantao ^[3]

Advanced Computing, Mathematics &, Data, Pacific Northwest National Laboratory, Richland, WA 99352,
Advanced Computing, Mathematics &, Data, Pacific Northwest National Laboratory, Richland, WA 99352,, Division of Applied Mathematics, Brown University, Providence, RI 02912,
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Significance The generalized Langevin equation (GLE) provides a precise description of coarse-grained variable dynamics in reduced dimension models. However, computation of the memory kernel poses a major challenge to the practical use of the GLE. This paper presents a data-driven approach to compute the memory kernel, relying on a hierarchy of parameterized rational approximations in terms of the Laplace transform, which can be expanded to arbitrarily high order as necessary. This parameterization makes it convenient to represent the GLE via an extended stochastic model where the memory term is eliminated by properly introducing auxiliary variables. The present method is well-suited for constructing reduced models for nonequilibrium properties of complex systems such as biomolecules, chemical reaction networks, and climate simulations.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: CM4; AC05-76RL01830

OSTI ID:: 1333885

Alternate ID(s):: OSTI ID: 1339841

Report Number(s):: PNNL-SA-118385

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Vol. 113 Journal Issue: 50; ISSN 0027-8424

Publisher:: Proceedings of the National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 88 works

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References (46)

Physics constrained nonlinear regression models for time series Majda, Andrew J.; Harlim, John Nonlinearity, Vol. 26, Issue 1 https://doi.org/10.1088/0951-7715/26/1/201	journal	November 2012
Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature: Treatment of the thermal bath Li, Xiantao; E., Weinan Physical Review B, Vol. 76, Issue 10 https://doi.org/10.1103/PhysRevB.76.104107	journal	September 2007
Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics Hoogerbrugge, P. J.; Koelman, J. M. V. A. Europhysics Letters (EPL), Vol. 19, Issue 3 https://doi.org/10.1209/0295-5075/19/3/001	journal	June 1992
Mori–Zwanzig formalism as a practical computational tool Hijón, Carmen; Español, Pep; Vanden-Eijnden, Eric Faraday Discuss., Vol. 144 https://doi.org/10.1039/B902479B	journal	January 2010
Extracting macroscopic dynamics: model problems and algorithms Givon, Dror; Kupferman, Raz; Stuart, Andrew Nonlinearity, Vol. 17, Issue 6 https://doi.org/10.1088/0951-7715/17/6/R01	journal	August 2004
Langevin Equation with Colored Noise for Constant-Temperature Molecular Dynamics Simulations Ceriotti, Michele; Bussi, Giovanni; Parrinello, Michele Physical Review Letters, Vol. 102, Issue 2 https://doi.org/10.1103/PhysRevLett.102.020601	journal	January 2009
Statistical Mechanics of Dissipative Particle Dynamics Español, P.; Warren, P. Europhysics Letters (EPL), Vol. 30, Issue 4 https://doi.org/10.1209/0295-5075/30/4/001	journal	May 1995
Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence Davtyan, Aram; Dama, James F.; Voth, Gregory A. The Journal of Chemical Physics, Vol. 142, Issue 15 https://doi.org/10.1063/1.4917454	journal	April 2015
A coarse-grained molecular dynamics model for crystalline solids Li, Xiantao International Journal for Numerical Methods in Engineering, Vol. 83, Issue 8-9 https://doi.org/10.1002/nme.2892	journal	August 2010
Generalized Langevin equation approach for atom/solid‐surface scattering: Collinear atom/harmonic chain model Adelman, S. A.; Doll, J. D. The Journal of Chemical Physics, Vol. 61, Issue 10 https://doi.org/10.1063/1.1681723	journal	November 1974
Bottom-up coarse-graining of a simple graphene model: The blob picture Kauzlarić, David; Meier, Julia T.; Español, Pep The Journal of Chemical Physics, Vol. 134, Issue 6 https://doi.org/10.1063/1.3554395	journal	February 2011
Calculation of effective interaction potentials from radial distribution functions: A reverse Monte Carlo approach Lyubartsev, Alexander P.; Laaksonen, Aatto Physical Review E, Vol. 52, Issue 4 https://doi.org/10.1103/PhysRevE.52.3730	journal	October 1995
Generalized Langevin dynamics simulations with arbitrary time‐dependent memory kernels Berkowitz, M.; Morgan, J. D.; McCammon, J. Andrew The Journal of Chemical Physics, Vol. 78, Issue 6 https://doi.org/10.1063/1.445244	journal	March 1983
THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method Kumar, Shankar; Rosenberg, John M.; Bouzida, Djamal Journal of Computational Chemistry, Vol. 13, Issue 8 https://doi.org/10.1002/jcc.540130812	journal	October 1992
Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel Baczewski, Andrew D.; Bond, Stephen D. The Journal of Chemical Physics, Vol. 139, Issue 4 https://doi.org/10.1063/1.4815917	journal	July 2013
Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach Wouters, Jeroen; Lucarini, Valerio Journal of Statistical Physics, Vol. 151, Issue 5 https://doi.org/10.1007/s10955-013-0726-8	journal	March 2013
Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics Chorin, Alexandre J.; Lu, Fei Proceedings of the National Academy of Sciences, Vol. 112, Issue 32 https://doi.org/10.1073/pnas.1512080112	journal	July 2015
A Multiscale Coarse-Graining Method for Biomolecular Systems Izvekov, Sergei; Voth, Gregory A. The Journal of Physical Chemistry B, Vol. 109, Issue 7 https://doi.org/10.1021/jp044629q	journal	February 2005
Problem reduction, renormalization, and memory Chorin, Alexandre; Stinis, Panagiotis Communications in Applied Mathematics and Computational Science, Vol. 1, Issue 1 https://doi.org/10.2140/camcos.2006.1.1	journal	January 2006
Generalized Langevin Equation with Fractional Gaussian Noise: Subdiffusion within a Single Protein Molecule Kou, S. C.; Xie, X. Sunney Physical Review Letters, Vol. 93, Issue 18 https://doi.org/10.1103/PhysRevLett.93.180603	journal	October 2004
Dynamics of an Inhomogeneously Coarse Grained Multiscale System Curtarolo, Stefano; Ceder, Gerbrand Physical Review Letters, Vol. 88, Issue 25 https://doi.org/10.1103/PhysRevLett.88.255504	journal	June 2002
A generalized Langevin dynamics approach to model solvent dynamics effects on proteins via a solvent-accessible surface. The carboxypeptidase A inhibitor protein as a model Oliva, Baldomero; Daura, Xavier; Querol, Enrique Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 105, Issue 2 https://doi.org/10.1007/s002140000183	journal	December 2000
Parametric reduced models for the nonlinear Schrödinger equation Harlim, John; Li, Xiantao Physical Review E, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevE.91.053306	journal	May 2015
Computation of the memory functions in the generalized Langevin models for collective dynamics of macromolecules Chen, Minxin; Li, Xiantao; Liu, Chun The Journal of Chemical Physics, Vol. 141, Issue 6 https://doi.org/10.1063/1.4892412	journal	August 2014
Nonlinear generalized Langevin equations Zwanzig, Robert Journal of Statistical Physics, Vol. 9, Issue 3 https://doi.org/10.1007/BF01008729	journal	November 1973
Dynamic friction on rigid and flexible bonds Berne, B. J.; Tuckerman, M. E.; Straub, John E. The Journal of Chemical Physics, Vol. 93, Issue 7 https://doi.org/10.1063/1.458647	journal	October 1990
Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism Li, Zhen; Bian, Xin; Li, Xiantao The Journal of Chemical Physics, Vol. 143, Issue 24 https://doi.org/10.1063/1.4935490	journal	December 2015
Transport, Collective Motion, and Brownian Motion Mori, Hazime Progress of Theoretical Physics, Vol. 33, Issue 3 https://doi.org/10.1143/PTP.33.423	journal	March 1965
Direct construction of mesoscopic models from microscopic simulations Lei, Huan; Caswell, Bruce; Karniadakis, George Em Physical Review E, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevE.81.026704	journal	February 2010
Time-Domain Methods for Diffusive Transport in Soft Matter Fricks, John; Yao, Lingxing; Elston, Timothy C. SIAM Journal on Applied Mathematics, Vol. 69, Issue 5 https://doi.org/10.1137/070695186	journal	January 2009
Modeling real dynamics in the coarse-grained representation of condensed phase systems Izvekov, Sergei; Voth, Gregory A. The Journal of Chemical Physics, Vol. 125, Issue 15 https://doi.org/10.1063/1.2360580	journal	October 2006
The relative entropy is fundamental to multiscale and inverse thermodynamic problems Shell, M. Scott The Journal of Chemical Physics, Vol. 129, Issue 14 https://doi.org/10.1063/1.2992060	journal	October 2008
Observation of a Power-Law Memory Kernel for Fluctuations within a Single Protein Molecule Min, Wei; Luo, Guobin; Cherayil, Binny J. Physical Review Letters, Vol. 94, Issue 19 https://doi.org/10.1103/PhysRevLett.94.198302	journal	May 2005
Dynamic solvent effects on activated chemical reactions. I. Classical effects of reaction path curvature Schenter, Gregory K.; McRae, Robin P.; Garrett, Bruce C. The Journal of Chemical Physics, Vol. 97, Issue 12 https://doi.org/10.1063/1.463970	journal	December 1992
A note on matrix-valued rational interpolants Zhu, Gong-Qin; Tan, Jie-Qing Journal of Computational and Applied Mathematics, Vol. 110, Issue 1 https://doi.org/10.1016/S0377-0427(99)00203-4	journal	October 1999
The Elementary Gaussian Processes Doob, J. L. The Annals of Mathematical Statistics, Vol. 15, Issue 3 https://doi.org/10.1214/aoms/1177731234	journal	September 1944
The derivation and approximation of coarse-grained dynamics from Langevin dynamics Ma, Lina; Li, Xiantao; Liu, Chun The Journal of Chemical Physics, Vol. 145, Issue 20 https://doi.org/10.1063/1.4967936	journal	November 2016
Colored-Noise Thermostats à la Carte Ceriotti, Michele; Bussi, Giovanni; Parrinello, Michele Journal of Chemical Theory and Computation, Vol. 6, Issue 4 https://doi.org/10.1021/ct900563s	journal	March 2010
Memory kernels from molecular dynamics Berkowitz, Max; Morgan, John D.; Kouri, Donald J. The Journal of Chemical Physics, Vol. 75, Issue 5 https://doi.org/10.1063/1.442269	journal	September 1981
Escaping free-energy minima Laio, A.; Parrinello, M. Proceedings of the National Academy of Sciences, Vol. 99, Issue 20 https://doi.org/10.1073/pnas.202427399	journal	September 2002
Deriving effective mesoscale potentials from atomistic simulations: Mesoscale Potentials from Atomistic Simulations Reith, Dirk; Pütz, Mathias; Müller-Plathe, Florian Journal of Computational Chemistry, Vol. 24, Issue 13 https://doi.org/10.1002/jcc.10307	journal	August 2003
Collective Langevin dynamics of conformational motions in proteins Lange, Oliver F.; Grubmüller, Helmut The Journal of Chemical Physics, Vol. 124, Issue 21 https://doi.org/10.1063/1.2199530	journal	June 2006
Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen Einstein, A. Annalen der Physik, Vol. 322, Issue 8 https://doi.org/10.1002/andp.19053220806	journal	January 1905
Computing generalized Langevin equations and generalized Fokker-Planck equations Darve, E.; Solomon, J.; Kia, A. Proceedings of the National Academy of Sciences, Vol. 106, Issue 27 https://doi.org/10.1073/pnas.0902633106	journal	June 2009
The fluctuation-dissipation theorem Kubo, R. Reports on Progress in Physics, Vol. 29, Issue 1 https://doi.org/10.1088/0034-4885/29/1/306	journal	January 1966
The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models Noid, W. G.; Chu, Jhih-Wei; Ayton, Gary S. The Journal of Chemical Physics, Vol. 128, Issue 24 https://doi.org/10.1063/1.2938860	journal	June 2008

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