Uncertainty quantification for generalized Langevin dynamics

Hall, Eric J.; Katsoulakis, Markos A.; Rey-Bellet, Luc

doi:10.1063/1.4971433

Uncertainty quantification for generalized Langevin dynamics

Journal Article · Wed Dec 14 00:00:00 EST 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4971433· OSTI ID:1465368

^[1]; Katsoulakis, Markos A. ^[2]; ^[2]

Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics; Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Massachusetts, Amherst, MA (United States). Dept. of Mathematics and Statistics

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0010723

OSTI ID:: 1465368

Alternate ID(s):: OSTI ID: 1336482

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 22 Vol. 145; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (61)

Open Classical Systems Rey-Bellet, Luc Lecture Notes in Mathematics https://doi.org/10.1007/3-540-33966-3_2	book	January 2006
Pathwise Sensitivity Analysis in Transient Regimes Arampatzis, Georgios; Katsoulakis, Markos A.; Pantazis, Yannis Mathematical Engineering https://doi.org/10.1007/978-3-319-18206-3_5	book	January 2015
Stochastic Differential Equations Øksendal, Bernt Universitext https://doi.org/10.1007/978-3-642-14394-6	book	January 2003
Applications of Malliavin calculus to Monte-Carlo methods in finance. II Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme Finance and Stochastics, Vol. 5, Issue 2 https://doi.org/10.1007/PL00013529	journal	April 2001
Convergence rates for steady-state derivative estimators L'Ecuyer, Pierre Annals of Operations Research, Vol. 39, Issue 1 https://doi.org/10.1007/bf02060938	journal	December 1992
On the Malliavin approach to Monte Carlo approximation of conditional expectations Bouchard, Bruno; Ekeland, Ivar; Touzi, Nizar Finance and Stochastics, Vol. 8, Issue 1 https://doi.org/10.1007/s00780-003-0109-0	journal	January 2004
Applications of Malliavin calculus to Monte Carlo methods in finance Fournié, Eric; Lasry, Jean-Michel; Lebuchoux, Jérôme Finance and Stochastics, Vol. 3, Issue 4 https://doi.org/10.1007/s007800050068	journal	August 1999
Multilevel hybrid split-step implicit tau-leap Ben Hammouda, Chiheb; Moraes, Alvaro; Tempone, Raúl Numerical Algorithms, Vol. 74, Issue 2 https://doi.org/10.1007/s11075-016-0158-z	journal	June 2016
Monte Carlo methods for security pricing Boyle, Phelim; Broadie, Mark; Glasserman, Paul Journal of Economic Dynamics and Control, Vol. 21, Issue 8-9 https://doi.org/10.1016/S0165-1889(97)00028-6	journal	June 1997
On approximation of functions by exponential sums Beylkin, Gregory; Monzón, Lucas Applied and Computational Harmonic Analysis, Vol. 19, Issue 1 https://doi.org/10.1016/j.acha.2005.01.003	journal	July 2005
Approximation by exponential sums revisited Beylkin, Gregory; Monzón, Lucas Applied and Computational Harmonic Analysis, Vol. 28, Issue 2 https://doi.org/10.1016/j.acha.2009.08.011	journal	March 2010
An effective screening design for sensitivity analysis of large models Campolongo, Francesca; Cariboni, Jessica; Saltelli, Andrea Environmental Modelling & Software, Vol. 22, Issue 10 https://doi.org/10.1016/j.envsoft.2006.10.004	journal	October 2007
A multivariate generalization of Prony's method Kunis, Stefan; Peter, Thomas; Römer, Tim Linear Algebra and its Applications, Vol. 490 https://doi.org/10.1016/j.laa.2015.10.023	journal	February 2016
Parameter estimation for exponential sums by approximate Prony method Potts, Daniel; Tasche, Manfred Signal Processing, Vol. 90, Issue 5 https://doi.org/10.1016/j.sigpro.2009.11.012	journal	May 2010
Malliavin Greeks without Malliavin calculus Chen, Nan; Glasserman, Paul Stochastic Processes and their Applications, Vol. 117, Issue 11 https://doi.org/10.1016/j.spa.2007.03.012	journal	November 2007
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
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
Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks Rathinam, Muruhan; Sheppard, Patrick W.; Khammash, Mustafa The Journal of Chemical Physics, Vol. 132, Issue 3 https://doi.org/10.1063/1.3280166	journal	January 2010
Efficient stochastic thermostatting of path integral molecular dynamics Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E. The Journal of Chemical Physics, Vol. 133, Issue 12 https://doi.org/10.1063/1.3489925	journal	September 2010
Efficient multiple time scale molecular dynamics: Using colored noise thermostats to stabilize resonances Morrone, Joseph A.; Markland, Thomas E.; Ceriotti, Michele The Journal of Chemical Physics, Vol. 134, Issue 1 https://doi.org/10.1063/1.3518369	journal	January 2011
Accelerating the convergence of path integral dynamics with a generalized Langevin equation Ceriotti, Michele; Manolopoulos, David E.; Parrinello, Michele The Journal of Chemical Physics, Vol. 134, Issue 8 https://doi.org/10.1063/1.3556661	journal	February 2011
A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics Pantazis, Yannis; Katsoulakis, Markos A. The Journal of Chemical Physics, Vol. 138, Issue 5 https://doi.org/10.1063/1.4789612	journal	February 2013
Comparison of finite difference based methods to obtain sensitivities of stochastic chemical kinetic models Srivastava, Rishi; Anderson, David F.; Rawlings, James B. The Journal of Chemical Physics, Vol. 138, Issue 7 https://doi.org/10.1063/1.4790650	journal	February 2013
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
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations Arampatzis, Georgios; Katsoulakis, Markos A. The Journal of Chemical Physics, Vol. 140, Issue 12 https://doi.org/10.1063/1.4868649	journal	March 2014
Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems Wolf, Elizabeth Skubak; Anderson, David F. The Journal of Chemical Physics, Vol. 142, Issue 3 https://doi.org/10.1063/1.4905332	journal	January 2015
Parametric sensitivity analysis for stochastic molecular systems using information theoretic metrics Tsourtis, Anastasios; Pantazis, Yannis; Katsoulakis, Markos A. The Journal of Chemical Physics, Vol. 143, Issue 1 https://doi.org/10.1063/1.4922924	journal	July 2015
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
Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc The Journal of Chemical Physics, Vol. 144, Issue 10 https://doi.org/10.1063/1.4943388	journal	March 2016
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
Factorial Sampling Plans for Preliminary Computational Experiments Morris, Max D. Technometrics, Vol. 33, Issue 2 https://doi.org/10.1080/00401706.1991.10484804	journal	May 1991
Model Comparison and Assessment for Single Particle Tracking in Biological Fluids Lysy, Martin; Pillai, Natesh S.; Hill, David B. Journal of the American Statistical Association, Vol. 111, Issue 516 https://doi.org/10.1080/01621459.2016.1158716	journal	October 2016
A simple framework to justify linear response theory Hairer, Martin; Majda, Andrew J. Nonlinearity, Vol. 23, Issue 4 https://doi.org/10.1088/0951-7715/23/4/008	journal	March 2010
Asymptotic analysis for the generalized Langevin equation Ottobre, M.; Pavliotis, G. A. Nonlinearity, Vol. 24, Issue 5 https://doi.org/10.1088/0951-7715/24/5/013	journal	April 2011
SPSens: a software package for stochastic parameter sensitivity analysis of biochemical reaction networks Sheppard, Patrick W.; Rathinam, Muruhan; Khammash, Mustafa Bioinformatics, Vol. 29, Issue 1 https://doi.org/10.1093/bioinformatics/bts642	journal	October 2012
Numerical Experiments on the Stochastic Behavior of a Lennard-Jones Gas System Stoddard, Spotswood D.; Ford, Joseph Physical Review A, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevA.8.1504	journal	September 1973
Generalized Langevin equation for solids. I. Rigorous derivation and main properties Kantorovich, L. Physical Review B, Vol. 78, Issue 9 https://doi.org/10.1103/PhysRevB.78.094304	journal	September 2008
Generalized Langevin equation for solids. II. Stochastic boundary conditions for nonequilibrium molecular dynamics simulations Kantorovich, L.; Rompotis, N. Physical Review B, Vol. 78, Issue 9 https://doi.org/10.1103/PhysRevB.78.094305	journal	September 2008
Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems Stella, L.; Lorenz, C. D.; Kantorovich, L. Physical Review B, Vol. 89, Issue 13 https://doi.org/10.1103/PhysRevB.89.134303	journal	April 2014
Applications of the generalized Langevin equation: Towards a realistic description of the baths Ness, H.; Stella, L.; Lorenz, C. D. Physical Review B, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevB.91.014301	journal	January 2015
Nonequilibrium processes from generalized Langevin equations: Realistic nanoscale systems connected to two thermal baths Ness, H.; Genina, A.; Stella, L. Physical Review B, Vol. 93, Issue 17 https://doi.org/10.1103/PhysRevB.93.174303	journal	May 2016
Anomalous diffusion: Exact solution of the generalized Langevin equation for harmonically bounded particle Viñales, A. D.; Despósito, M. A. Physical Review E, Vol. 73, Issue 1 https://doi.org/10.1103/PhysRevE.73.016111	journal	January 2006
Subdiffusive behavior in a trapping potential: Mean square displacement and velocity autocorrelation function Despósito, M. A.; Viñales, A. D. Physical Review E, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevE.80.021111	journal	August 2009
Nonergodicity Mimics Inhomogeneity in Single Particle Tracking Lubelski, Ariel; Sokolov, Igor M.; Klafter, Joseph Physical Review Letters, Vol. 100, Issue 25 https://doi.org/10.1103/PhysRevLett.100.250602	journal	June 2008
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
Nuclear Quantum Effects in Solids Using a Colored-Noise Thermostat Ceriotti, Michele; Bussi, Giovanni; Parrinello, Michele Physical Review Letters, Vol. 103, Issue 3 https://doi.org/10.1103/PhysRevLett.103.030603	journal	July 2009
Malliavin Weight Sampling for Computing Sensitivity Coefficients in Brownian Dynamics Simulations Warren, Patrick B.; Allen, Rosalind J. Physical Review Letters, Vol. 109, Issue 25 https://doi.org/10.1103/PhysRevLett.109.250601	journal	December 2012
Direct Computation of Dynamical Response by Molecular Dynamics: The Mobility of a Charged Lennard-Jones Particle Ciccotti, G.; Jacucci, G. Physical Review Letters, Vol. 35, Issue 12 https://doi.org/10.1103/PhysRevLett.35.789	journal	September 1975
Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids Mason, T. G.; Weitz, D. A. Physical Review Letters, Vol. 74, Issue 7 https://doi.org/10.1103/PhysRevLett.74.1250	journal	February 1995
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
Statistical challenges in microrheology: STATISTICAL CHALLENGES IN MICRORHEOLOGY Didier, Gustavo; McKinley, Scott A.; Hill, David B. Journal of Time Series Analysis, Vol. 33, Issue 5 https://doi.org/10.1111/j.1467-9892.2012.00792.x	journal	May 2012
An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains Anderson, David F. SIAM Journal on Numerical Analysis, Vol. 50, Issue 5 https://doi.org/10.1137/110849079	journal	January 2012
Path-Space Information Bounds for Uncertainty Quantification and Sensitivity Analysis of Stochastic Dynamics Dupuis, Paul; Katsoulakis, Markos A.; Pantazis, Yannis SIAM/ASA Journal on Uncertainty Quantification, Vol. 4, Issue 1 https://doi.org/10.1137/15M1025645	journal	January 2016
Likelihood ratio gradient estimation for stochastic systems Glynn, Peter W. Communications of the ACM, Vol. 33, Issue 10 https://doi.org/10.1145/84537.84552	journal	October 1990
Parametric sensitivity analysis for biochemical reaction networks based on pathwise information theory Pantazis, Yannis; Katsoulakis, Markos A.; Vlachos, Dionisios G. BMC Bioinformatics, Vol. 14, Issue 1 https://doi.org/10.1186/1471-2105-14-311	journal	January 2013
Sensitivity Anaysis as an Ingredient of Modeling Campolongo, F.; Tarantola, S.; Saltelli, A. Statistical Science, Vol. 15, Issue 4 https://doi.org/10.1214/ss/1009213004	journal	November 2000
Some Guidelines and Guarantees for Common Random Numbers Glasserman, Paul; Yao, David D. Management Science, Vol. 38, Issue 6 https://doi.org/10.1287/mnsc.38.6.884	journal	June 1992
Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems Zazanis, Michael A.; Suri, Rajan Operations Research, Vol. 41, Issue 4 https://doi.org/10.1287/opre.41.4.694	journal	August 1993
On the Convergence Rates of IPA and FDC Derivative Estimators L'Ecuyer, Pierre; Perron, Gaétan Operations Research, Vol. 42, Issue 4 https://doi.org/10.1287/opre.42.4.643	journal	August 1994
Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks Arampatzis, Georgios; Katsoulakis, Markos A.; Pantazis, Yannis PLOS ONE, Vol. 10, Issue 7 https://doi.org/10.1371/journal.pone.0130825	journal	July 2015
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

Cited By (3)

Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations Bockius, Niklas; Shea, Jeanine; Jung, Gerhard arXiv https://doi.org/10.48550/arxiv.2101.02657	text	January 2021
Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion Lim, Soon Hoe; Wehr, Jan; Lewenstein, Maciej Annales Henri Poincaré, Vol. 21, Issue 6 https://doi.org/10.1007/s00023-020-00889-2	journal	February 2020
Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation Rossi, Mariana; Kapil, Venkat; Ceriotti, Michele The Journal of Chemical Physics, Vol. 148, Issue 10 https://doi.org/10.1063/1.4990536	journal	March 2018

Similar Records

Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures

Journal Article · Wed May 01 00:00:00 EDT 2013 · Journal of Computational Physics · OSTI ID:22233570

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks

Journal Article · Thu Jul 09 20:00:00 EDT 2015 · PLoS ONE · OSTI ID:1456883

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

Journal Article · Thu Mar 10 19:00:00 EST 2016 · Journal of Chemical Physics · OSTI ID:1470323

Related Subjects

97 MATHEMATICS AND COMPUTING

Uncertainty quantification for generalized Langevin dynamics

Citation Formats

References (61)

Cited By (3)

Similar Records

Related Subjects