A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics

Journal of Chemical Physics

Volumn 138, Issue 5, 2013, Pages

  Pantazis, Yannis ^a   Katsoulakis, Markos A ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIRECT MONTE CARLO SIMULATIONS; FISHER INFORMATION; HIGH DIMENSIONALITY; HIGH-DIMENSIONAL; HIGH-DIMENSIONAL PROBLEMS; KINETIC MONTE CARLO MODEL; LANGEVIN PARTICLES; METASTABILITIES; NON-GAUSSIAN; NONEQUILIBRIUM SYSTEM; PATH SPACE; RELATIVE ENTROPY RATES; SPATIALLY DISTRIBUTED MODELS; STATIONARY REGIME; STOCHASTIC DYNAMICS;

DYNAMICS; FISHER INFORMATION MATRIX; MONTE CARLO METHODS; PROBABILITY DISTRIBUTIONS; SENSITIVITY ANALYSIS; STATISTICAL MECHANICS; STOCHASTIC SYSTEMS;

SIGNAL THEORY;

ARTICLE; ENTROPY; KINETICS; MOLECULAR DYNAMICS; MONTE CARLO METHOD; STATISTICS;

ENTROPY; KINETICS; MOLECULAR DYNAMICS SIMULATION; MONTE CARLO METHOD; STOCHASTIC PROCESSES;

MLCS; MLOWN;

EID: 84873673530     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4789612     Document Type: Article

References (60)

1. R. Gunawan, Y. Cao, L. Petzold, and F. J. Doyle III, " Sensitivity analysis of discrete stochastic systems.," Biophys. J. 88, 2530-2540 (2005). 10.1529/biophysj.104.053405
2. M. Nakayama, A. Goyal, and P. W. Glynn, " Likelihood ratio sensitivity analysis for Markovian models of highly dependable systems.," Stoch. Models 10, 701-717 (1994). 10.1080/15326349408807318
3. S. Plyasunov and A. P. Arkin, " Efficient stochastic sensitivity analysis of discrete event systems.," J. Comput. Phys. 221, 724-738 (2007). 10.1016/j.jcp.2006.06.047
4. D. Kim, B. Debusschere, and H. Najm, " Spectral methods for parametric sensitivity in stochastic dynamical systems.," Biophys. J. 92, 379-393 (2007). 10.1529/biophysj.106.085084
5. M. Rathinam, P. W. Sheppard, and M. Khammash, " Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks.," J. Chem. Phys. 132, 034103 (2010). 10.1063/1.3280166
6. C. Wu, D. J. Schmidt, C. Wolverton, and W. F. Schneider, " Accurate coverage-dependence incorporated into first-principles kinetic models: Catalytic NO oxidation on Pt (111).," J. Catal. 286, 88-94 (2012). 10.1016/j.jcat.2011.10.020
7. H. Liu, W. Chen, and A. Sudjianto, " Relative entropy based method for probabilistic sensitivity analysis in engineering design.," J. Mech. Des. 128, 326-336 (2006). 10.1115/1.2159025
8. N. Lüdtke, S. Panzeri, M. Brown, D. S. Broomhead, J. Knowles, M. A. Montemurro, and D. B. Kell, " Information-theoretic sensitivity analysis: a general method for credit assignment in complex networks.," J. R. Soc., Interface 5, 223-235 (2008). 10.1098/rsif.2007.1079
9. A. J. Majda and B. Gershgorin, " Quantifying uncertainty in climate change science through empirical information theory.," Proc. Natl. Acad. Sci. U.S.A. 107, 14958-14963 (2010). 10.1073/pnas.1007009107
10. A. J. Majda and B. Gershgorin, " Improving model fidelity and sensitivity for complex systems through empirical information theory.," Proc. Natl. Acad. Sci. U.S.A. 108, 10044-10049 (2011). 10.1073/pnas.1105174108
11. M. Komorowski, M. J. Costa, D. A. Rand, and M. P. H. Stumpf, " Sensitivity, robustness, and identifiability in stochastic chemical kinetics models.," Proc. Natl. Acad. Sci. U.S.A. 108, 8645-8650 (2011). 10.1073/pnas.1015814108
12. C. R. Doering, K. V. Sargsyan, L. M. Sander, and E. Vanden-Eijnden, " Asymptotics of rare events in birth-death processes bypassing the exact solutions.," J. Phys.: Condens. Matter 19, 065145 (2007). 10.1088/0953-8984/19/6/065145
13. P. Hanggi, H. Grabert, P. Talkner, and H. Thomas, " Bistable systems: Master equation versus Fokker-Planck modeling.," Phys. Rev. A 29, 371-378 (1984). 10.1103/PhysRevA.29.371
14. M. A. Katsoulakis, A. J. Majda, and A. Sopasakis, " Intermittency, metastability and coarse graining for coupled deterministic-stochastic lattice systems.," Nonlinearity 19, 1021-1047 (2006). 10.1088/0951-7715/19/5/002
15. A. Chatterjee and D. G. Vlachos, " An overview of spatial microscopic and accelerated kinetic Monte Carlo methods for materials' simulation.," J. Comput.-Aided Mater. Des. 14, 253-308 (2007). 10.1007/s10820-006-9042-9
16. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).
17. M. A. Katsoulakis and J. Trashorras, " Information loss in coarse-graining of stochastic particle dynamics.," J. Stat. Phys. 122, 115-135 (2006). 10.1007/s10955-005-8063-1
18. M. A. Katsoulakis, L. Rey-Bellet, P. Plecháč, and D. K. Tsagkarogiannis, " Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems.," ESAIM-Math. Modell. Numer. Anal. 41, 627-660 (2007). 10.1051/m2an:2007032
19. M. Arnst and R. Ghanem, " Probabilistic equivalence and stochastic model reduction in multiscale analysis.," Comput. Methods Appl. Mech. Eng. 197, 3584-3592 (2008). 10.1016/j.cma.2008.03.016
20. C. Kipnis and C. Landim, Scaling Limits of Interacting Particle Systems (Springer-Verlag, 1999).
21. C. Maes, F. Redig, and A. V. Moffaert, " On the definition of entropy production, via examples.," J. Math. Phys. 41, 1528-1553 (2000). 10.1063/1.533195
22. A. J. Majda, R. V. Abramov, and M. J. Grote, Information Theory and Stochastics for Multiscale Nonlinear Systems, CRM Monograph Series (American Mathematical Society, 2005).
23. S. K. Rao, R. Imam, K. Ramanathan, and S. Pushpavanam, " Sensitivity analysis and kinetic parameter estimation in a three way catalytic converter.," Ind. Eng. Chem. Res. 48, 3779-3790 (2009). 10.1021/ie801244w
24. R. Braatz, R. Alkire, E. Seebauer, E. Rusli, R. Gunawan, T. Drews, X. Li, and Y. He, " Perspectives on the design and control of multiscale systems.," J. Process Control 16, 193-204 (2006). 10.1016/j.jprocont.2005. 06.001
25. T. Rothenberg, " Identification in parametric models.," Econometrica 39, 577-0591 (1971). 10.2307/1913267
26. A. F. Emery and A. V. Nenarokomov, " Optimal experiment design.," Meas. Sci. Technol. 9, 864-876 (1998). 10.1088/0957-0233/9/6/003
27. V. Prasad, A. M. Karim, Z. Ulissi, M. Zagrobelny, and D. G. Vlachos, " High throughput multiscale modeling for design of experiments, catalysts, and reactors: Application to hydrogen production from ammonia.," Chem. Eng. Sci. 65, 240-246 (2010). 10.1016/j.ces.2009.05.054
28. D. T. Gillespie, " Approximated accelerated stochastic simulation of chemically reacting systems.," J. Chem. Phys. 115, 1716-1733 (2001). 10.1063/1.1378322
29. S. Plimpton, C. Battaile, M. Chandross, L. Holm, A. Thompson, V. Tikare, G. Wagner, E. Webb, X. Zhou, C. G. Cardona, and A. Slepoy, " Crossing the mesoscale no-man's land via parallel kinetic Monte Carlo.," Tech. Rep. SAND2009-6226 (Sandia National Laboratory, 2009).
30. S. J. Plimpton and A. P. Thompson, " Computational aspects of many-body potentials.," MRS Bull. 37, 513-521 (2012). 10.1557/mrs.2012.96
31. G. Arampatzis, M. A. Katsoulakis, P. Plechac, M. Taufer, and L. Xu, " Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms.," J. Comp. Phys. 231, 7795-7814 (2012). 10.1016/j.jcp.2012.07.017
32. E. W. Hansen and M. Neurock, " First-principles-based Monte Carlo simulation of ethylene hydrogenation kinetics on Pd.," J. Catal. 196, 241-252 (2000). 10.1006/jcat.2000.3018
33. H. Meskine, S. Matera, M. Scheffler, K. Reuter, and H. Metiu, " Examination of the concept of degree of rate control by first-principles kinetic Monte Carlo simulations.," Surf. Sci. 603 (10-12), 1724-1730 (2009). 10.1016/j.susc.2008.08.036
34. M. Stamatakis, Y. Chen, and D. G. Vlachos, " First-principles-based kinetic Monte Carlo simulation of the structure sensitivity of the water-gas shift reaction on Platinum surfaces.," J. Phys. Chem. C 115 (50), 24750-24762 (2011). 10.1021/jp2071869
35. R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes: I II (Springer, 1977).
36. M. E. Dumitrescu, " Some informational properties of Markov pure-jump processes.," Časopis pro pěstování matematiky 113, 429-434 (1988).
37. L. Wen and Y. Weiguo, " An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains.," Stochastic Proc. Appl. 61, 129-145 (1996). 10.1016/0304-4149(95)00068-2
38. N. Limnios and G. Oprisan, Semi-Markov Processes and Reliability (Springer, 2001).
39. K. A. Lutz and A. S. Kiremidjian, " A generalized semi-Markov process for modeling spatially and temporally dependent earthquakes.," Tech. Rep. 104 (The J. A. Blume Earthquake Engineering Center, 1993).
40. J. Janssen and R. Manca, Applied Semi-Markov Processes (Springer, 2006).
41. V. Girardin and N. Limnios, " On the entropy for semi-Markov processes.," J. Appl. Probab. 40, 1060-1068 (2003). 10.1239/jap/1067436100
42. D. T. Gillespie, " A general method for numerically simulating the stochastic time evolution of coupled chemical reactions.," J. Comput. Phys. 22, 403-434 (1976). 10.1016/0021-9991(76)90041-3
43. F. Schlögl, " Chemical reaction models for nonequilibrium phase transition.," Z. Phys. 253, 147-161 (1972). 10.1007/BF01379769
44. M. Vellela and H. Qian, " Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited.," J. R. Soc., Interface 6, 925-940 (2009). 10.1098/rsif.2008. 0476
45. C. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences (Springer, 1985).
46. A. Degasperi and S. Gilmore, " Sensitivity analysis of stochastic models of bistable biochemical reactions.," SFM 2008, 1-20.
47. D. C. Rapaport, The Art of Molecular Dynamics Simulations (Cambridge University Press, 1995).
48. T. Schlick, Molecular Modeling and Simulation (Springer, 2002).
49. D. Frenkel and B. Smit, Understanding Molecular Simulation, From Algorithms to Applications (Academic, 2002).
50. T. Lelievre, M. Rousset, and G. Stoltz, Free Energy Computations: A Mathematical Perspective (Imperial College Press, 2010).
51. W. Ebeling and L. Schimansky-Geier, " Swarm dynamics, attractors and bifurcations of active Brownian motion.," Eur. Phys. J. Spec. Top. 157, 17-31 (2008). 10.1140/epjst/e2008-00627-9
52. A. Scemama, T. Lelièvre, G. Stoltz, E. Cancès, and M. Caffarel, " An efficient sampling algorithm for variational Monte-Carlo.," J. Chem. Phys. 125, 114105 (2006). 10.1063/1.2354490
53. E. Cancès, F. Legoll, and G. Stoltz, " Theoretical and numerical comparison of sampling methods for molecular dynamics.," Math. Modell. Numer. Anal. 41, 351-390 (2007). 10.1051/m2an:2007014
54. I. Kaplan, Handbook of Molecular Physics and Quantum Chemistry (Wiley, 2003).
55. J. L. Lebowitz and H. Spohn, " A Gallavotti-Cohen type symmetry in the large deviation functional for stochastic dynamics.," J. Stat. Phys. 95, 333-365 (1999). 10.1023/A:1004589714161
56. C. R. Sweet, S. Chatterjee, Z. Xu, K. Bisordi, E. D. Rosen, and M. Alber, " Modelling platelet-blood flow interaction using the subcellular element Langevin method.," J. R. Soc., Interface 8, 1760-1771 (2011). 10.1098/rsif.2011.0180
57. A. Brunger, C. B. Brooks, and M. Karplus, " Stochastic boundary conditions for molecular dynamics simulations of ST2 water.," Chem. Phys. Lett. 105, 495-500 (1984). 10.1016/0009-2614(84)80098-6
58. R. M. Ziff, E. Gulari, and Y. Barshad, " Kinetic phase transitions in an irreversible surface-reaction model.," Phys. Rev. Lett. 56, 2553 (1986). 10.1103/PhysRevLett.56.2553
59. K. Chan, A. Saltelli, and S. Tarantola, " Sensitivity analysis of model output: variance-based methods make the difference.," in Proceedings of the 29th Conference on Winter Simulation (IEEE Conference Publications, Atlanta, USA, 1997), pp. 261-268.
60. A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola, Global Sensitivity Analysis. The Primer (Wiley, 2008).