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01.08.2013 | Focus

Reliable kinetic Monte Carlo simulation based on random set sampling

verfasst von: Yan Wang

Erschienen in: Soft Computing | Ausgabe 8/2013

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Abstract

Kinetic Monte Carlo (KMC) method has been widely used in simulating rare events such as chemical reactions or phase transitions. Yet lack of complete knowledge of transitions and the associated rates is one major challenge for accurate KMC predictions. In this paper, a reliable KMC (R-KMC) mechanism is proposed in which sampling is based on random sets instead of random numbers to improve the robustness of KMC results. In R-KMC, rates or propensities are interval estimates instead of precise numbers. A multi-event algorithm based on generalized interval probability is developed. The weak convergence of the multi-event algorithm towards the traditional KMC is demonstrated with a generalized Chapman–Kolmogorov equation.

Vorheriger Artikel Managing uncertainty and discontinuous condition numbers in geometric computation

Nächster Artikel An overview of C-XSC as a tool for interval arithmetic and its application in computing verified uncertain probabilistic models under Dempster–Shafer theory

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Auger A, Chatelain P, Koumoutsakos P (2006) R-leaping: accelerating the stochastic simulation algorithm by reaction leaps. J Chem Phys 125(8):084103. doi:10.1063/1.2218339 CrossRef

Berry H (2002) Monte Carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation. Biophys J 83(4):1891–1901. doi:10.1016/s0006-3495(02)73953-2 CrossRef

Blue J, Beichl I, Sullivan F (1995) Faster Monte Carlo simulations. Phys Rev E 51(2):R867–R868. doi:10.1103/PhysRevE.51.R867 CrossRef

Bratsun D (2005) Delay-induced stochastic oscillations in gene regulation. Proc Natl Acad Sci 102(41):14593–14598. doi:10.1073/pnas.0503858102 CrossRef

Burrage K, Hancock J, Leier A, Nicolau DV (2007) Modelling and simulation techniques for membrane biology. Brief Bioinform 8(4):234–244. doi:10.1093/bib/bbm033 CrossRef

Cai X, Xu Z (2007) K-leap method for accelerating stochastic simulation of coupled chemical reactions. J Chem Phys 126(7):074102. doi:10.1063/1.2436869 CrossRef

Chatterjee A, Vlachos DG (2007) An overview of spatial microscopic and accelerated kinetic Monte Carlo methods. J Comput Aid Mater Des 14(2):253–308. doi:10.1007/s10820-006-9042-9 CrossRef

Chatterjee A, Voter AF (2010) Accurate acceleration of kinetic Monte Carlo simulations through the modification of rate constants. J Chem Phys 132(19):194101. doi:10.1063/1.3409606 CrossRef

Chatterjee A, Vlachos DG, Katsoulakis MA (2005) Binomial distribution based τ-leap accelerated stochastic simulation. J Chem Phys 122(2):024112. doi:10.1063/1.1833357 CrossRef

Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38(2):325–339. doi:10.1214/aoms/1177698950 MathSciNetMATHCrossRef

Dimitrova NS, Markov SM, Popova ED (1992) Extended interval arithmetics: new results and applications. In: Atanassova L, Herzberger J (eds) Computer arithmetic and enclosure methods. North-holland, Amsterdam, pp 225–232

Dubois D, Prade HM (1988) Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New YorkMATHCrossRef

E W, Liu D, Vanden-Eijnden E (2007) Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. J Comput Phys 221(1):158–180. doi:10.1016/j.jcp.2006.06.019 MathSciNetMATHCrossRef

Ferson S, Kreinovick V, Ginzburg L, Myers DS, Sentz F (2003) Constructing probability boxes and Dempster-Shafer structures. Sandia National Laboratories, Albuquerque (SAND2002-4015)

Gardeñes E, Sainz MÁ, Jorba L, Calm R, Estela R, Mielgo H, Trepat A (2001) Reliab Comput 7(2):77–111. doi:10.1023/a:1011465930178 MathSciNetMATHCrossRef

Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22(4):403–434. doi:10.1016/0021-9991(76)90041-3 MathSciNetCrossRef

Gillespie DT (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 115(4):1716. doi:10.1063/1.1378322 CrossRef

Haseltine EL, Rawlings JB (2002) Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J Chem Phys 117(15):6959. doi:10.1063/1.1505860 CrossRef

Henkelman G, Jónsson H (2001) Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J Chem Phys 115(21):9657. doi:10.1063/1.1415500 CrossRef

Katsoulakis MA, Majda AJ, Vlachos DG (2003) Coarse-grained stochastic processes for microscopic lattice systems. Proc Natl Acad Sci 100(3):782–787. doi:10.1073/pnas.242741499 MathSciNetMATHCrossRef

Kaucher E (1980) Interval analysis in the extended interval space IR. In: Computing supplementa, vol 2. pp 33–49

Kierzek AM (2002) STOCKS: stochastic kinetic simulations of biochemical systems with Gillespie algorithm. Bioinformatics 18(3):470–481. doi:10.1093/bioinformatics/18.3.470 CrossRef

Kuznetsov VP (1995) Interval methods for processing statistical characteristics. In: International workshop on applications of interval computations, El Paso

Maksym PA (1988) Fast Monte Carlo simulation of MBE growth. Semicond Sci Technol 3(6):594–596. doi:10.1088/0268-1242/3/6/014 CrossRef

Markov S (1979) Calculus for interval functions of a real variable. Computing 22(4):325–337. doi:10.1007/bf02265313 MathSciNetMATHCrossRef

Mei D, Xu L, Henkelman G (2009) Potential energy surface of methanol decomposition on Cu(110). J Phys Chem C 113(11):4522–4537. doi:10.1021/jp808211q CrossRef

Molchanov IS (2005) Theory of random sets. Probability and its applications. Springer, London

Möller B, Beer M (2004) Fuzzy randomness: uncertainty in civil engineering and computational mechanics. Springer, BerlinCrossRef

Neumaier A (2004) Clouds, fuzzy sets, and probability intervals. Reliab Comput 10(4):249–272. doi:10.1023/B:REOM.0000032114.08705.cd MathSciNetMATHCrossRef

Picioreanu C, van Loosdrecht MCM, Curtis TP, Scott K (2010) Model based evaluation of the effect of pH and electrode geometry on microbial fuel cell performance. Bioelectrochemistry 78(1):8–24. doi:10.1016/j.bioelechem.2009.04.009 CrossRef

Rathinam M, Petzold LR, Cao Y, Gillespie DT (2003) Stiffness in stochastic chemically reacting systems: the implicit tau-leaping method. J Chem Phys 119(24):12784. doi:10.1063/1.1627296 CrossRef

Schnell S, Turner TE (2004) Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog Biophys Mol Biol 85(2–3):235–260. doi:10.1016/j.pbiomolbio.2004.01.012 CrossRef

Schulze T (2002) Kinetic Monte Carlo simulations with minimal searching. Phys Rev E 65(3):036704. doi:10.1103/PhysRevE.65.036704 CrossRef

Shafer G (1976) A mathematical theory of evidence. Princeton University Press, PrincetonMATH

Sörensen MR, Voter AF (2000) Temperature-accelerated dynamics for simulation of infrequent events. J Chem Phys 112(21):9599. doi:10.1063/1.481576 CrossRef

SPPARKS (2009) Kinetic Monte Carlo simulator. http://www.cs.sandia.gov/~sjplimp/spparks.html

Tian T, Burrage K (2004) Binomial leap methods for simulating stochastic chemical kinetics. J Chem Phys 121(21):10356. doi:10.1063/1.1810475 CrossRef

Trushin O, Karim A, Kara A, Rahman T (2005) Self-learning kinetic Monte Carlo method: application to Cu(111). Phys Rev B 72(11) doi:10.1103/PhysRevB.72.115401

Voter A (1997) Hyperdynamics: accelerated molecular dynamics of infrequent events. Phys Rev Lett 78(20):3908–3911. doi:10.1103/PhysRevLett.78.3908 CrossRef

Voter A (1998) Parallel replica method for dynamics of infrequent events. Phys Rev B 57(22):R13985–R13988. doi:10.1103/PhysRevB.57.R13985 CrossRef

Walley P (1991) Statistical reasoning with imprecise probabilities. In: Monographs on statistics and applied probability, 1st edn. Chapman and Hall, London

Wang Y (2010) Imprecise probabilities based on generalised intervals for system reliability assessment. Int J Reliab Saf 4(4):319. doi:10.1504/ijrs.2010.035572 CrossRef

Weichselberger K (2000) The theory of interval-probability as a unifying concept for uncertainty. Int J Approx Reason 24(2–3):149–170. doi:10.1016/s0888-613x(00)00032-3 MathSciNetMATHCrossRef

Zeng Y, Choo YF, Kim B-H, Wu P (2010) Modelling and simulation of two-chamber microbial fuel cell. J Pow Sources 195(1):79–89. doi:10.1016/j.jpowsour.2009.06.101 CrossRef

Titel: Reliable kinetic Monte Carlo simulation based on random set sampling
verfasst von: Yan Wang
Publikationsdatum: 01.08.2013
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 8/2013
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-013-1013-y

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