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Title: Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling

Abstract

Kinetic Monte Carlo (KMC) simulation provides insights into catalytic reactions unobtainable with either experiments or mean-field microkinetic models. Sensitivity analysis of KMC models assesses the robustness of the predictions to parametric perturbations and identifies rate determining steps in a chemical reaction network. Stiffness in the chemical reaction network, a ubiquitous feature, demands lengthy run times for KMC models and renders efficient sensitivity analysis based on the likelihood ratio method unusable. We address the challenge of efficiently conducting KMC simulations and performing accurate sensitivity analysis in systems with unknown time scales by employing two acceleration techniques: rate constant rescaling and parallel processing. We develop statistical criteria that ensure sufficient sampling of non-equilibrium steady state conditions. Our approach provides the twofold benefit of accelerating the simulation itself and enabling likelihood ratio sensitivity analysis, which provides further speedup relative to finite difference sensitivity analysis. As a result, the likelihood ratio method can be applied to real chemistry. We apply our methodology to the water-gas shift reaction on Pt(111).

Authors:
 [1];  [1]; ORCiD logo [1]
  1. Univ. of Delaware, Newark, DE (United States)
Publication Date:
Research Org.:
Univ. of Delaware, Newark, DE (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1512927
Alternate Identifier(s):
OSTI ID: 1402107
Grant/Contract Number:  
[SC0010549]
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
[ Journal Volume: 147; Journal Issue: 16]; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Núñez, M., Robie, T., and Vlachos, D. G. Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling. United States: N. p., 2017. Web. doi:10.1063/1.4998926.
Núñez, M., Robie, T., & Vlachos, D. G. Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling. United States. doi:10.1063/1.4998926.
Núñez, M., Robie, T., and Vlachos, D. G. Mon . "Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling". United States. doi:10.1063/1.4998926. https://www.osti.gov/servlets/purl/1512927.
@article{osti_1512927,
title = {Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling},
author = {Núñez, M. and Robie, T. and Vlachos, D. G.},
abstractNote = {Kinetic Monte Carlo (KMC) simulation provides insights into catalytic reactions unobtainable with either experiments or mean-field microkinetic models. Sensitivity analysis of KMC models assesses the robustness of the predictions to parametric perturbations and identifies rate determining steps in a chemical reaction network. Stiffness in the chemical reaction network, a ubiquitous feature, demands lengthy run times for KMC models and renders efficient sensitivity analysis based on the likelihood ratio method unusable. We address the challenge of efficiently conducting KMC simulations and performing accurate sensitivity analysis in systems with unknown time scales by employing two acceleration techniques: rate constant rescaling and parallel processing. We develop statistical criteria that ensure sufficient sampling of non-equilibrium steady state conditions. Our approach provides the twofold benefit of accelerating the simulation itself and enabling likelihood ratio sensitivity analysis, which provides further speedup relative to finite difference sensitivity analysis. As a result, the likelihood ratio method can be applied to real chemistry. We apply our methodology to the water-gas shift reaction on Pt(111).},
doi = {10.1063/1.4998926},
journal = {Journal of Chemical Physics},
number = [16],
volume = [147],
place = {United States},
year = {2017},
month = {10}
}

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Cited by: 6 works
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Figures / Tables:

FIG. 1 FIG. 1: Ratio of the variance of the estimate of the mean of a property and the variance of the property itself [i.e., the left-hand side of Eq. (6)] as a function of the length of the interval used for averaging (t̃) and the number of replicate trajectories (ntraj). Datamore » points show the variances of reaction rates. Simulation details are in Sec. SIIa of the supplementary material.« less

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Works referenced in this record:

Accurate coverage-dependence incorporated into first-principles kinetic models: Catalytic NO oxidation on Pt (111)
journal, February 2012


Likelihood Ratio Sensitivity Analysis for Markovian Models of Highly Dependable Systems
journal, February 1994

  • Nakayama, Marvin K.; Goyal, Ambuj; Glynn, Peter W.
  • Operations Research, Vol. 42, Issue 1
  • DOI: 10.1287/opre.42.1.137

A graph-theoretical kinetic Monte Carlo framework for on-lattice chemical kinetics
journal, June 2011

  • Stamatakis, Michail; Vlachos, Dionisios G.
  • The Journal of Chemical Physics, Vol. 134, Issue 21
  • DOI: 10.1063/1.3596751

Distinctions between Supported Au and Pt Catalysts for CO Oxidation: Insights from DFT Study
journal, October 2013

  • Cai, Qiuxia; Wang, Xinde; Wang, Jian-guo
  • The Journal of Physical Chemistry C, Vol. 117, Issue 41
  • DOI: 10.1021/jp406557f

SQERTSS: Dynamic rank based throttling of transition probabilities in kinetic Monte Carlo simulations
journal, October 2017

  • Danielson, Thomas; Sutton, Jonathan E.; Hin, Céline
  • Computer Physics Communications, Vol. 219
  • DOI: 10.1016/j.cpc.2017.05.016

Avoiding negative populations in explicit Poisson tau-leaping
journal, August 2005

  • Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 123, Issue 5
  • DOI: 10.1063/1.1992473

Adsorption Energy Correlations at the Metal–Support Boundary
journal, June 2017


Thermodynamic Consistency in Microkinetic Development of Surface Reaction Mechanisms
journal, November 2003

  • Mhadeshwar, A. B.; Wang, H.; Vlachos, D. G.
  • The Journal of Physical Chemistry B, Vol. 107, Issue 46
  • DOI: 10.1021/jp034954y

Density Functional Kinetic Monte Carlo Simulation of Water–Gas Shift Reaction on Cu/ZnO
journal, February 2013

  • Yang, Liu; Karim, Altaf; Muckerman, James T.
  • The Journal of Physical Chemistry C, Vol. 117, Issue 7
  • DOI: 10.1021/jp3114286

Stochastic averaging and sensitivity analysis for two scale reaction networks
journal, February 2016

  • Hashemi, Araz; Núñez, Marcel; Plecháč, Petr
  • The Journal of Chemical Physics, Vol. 144, Issue 7
  • DOI: 10.1063/1.4942008

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting
journal, March 2012

  • Warren, Patrick B.; Allen, Rosalind J.
  • The Journal of Chemical Physics, Vol. 136, Issue 10
  • DOI: 10.1063/1.3690092

Efficient stochastic sensitivity analysis of discrete event systems
journal, February 2007


Steam and dry reforming of methane on Rh: Microkinetic analysis and hierarchy of kinetic models
journal, October 2008


Steady state likelihood ratio sensitivity analysis for stiff kinetic Monte Carlo simulations
journal, January 2015

  • Núñez, M.; Vlachos, D. G.
  • The Journal of Chemical Physics, Vol. 142, Issue 4
  • DOI: 10.1063/1.4905957

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method
journal, December 2003

  • Rathinam, Muruhan; Petzold, Linda R.; Cao, Yang
  • The Journal of Chemical Physics, Vol. 119, Issue 24
  • DOI: 10.1063/1.1627296

Parallel kinetic Monte Carlo simulation framework incorporating accurate models of adsorbate lateral interactions
journal, December 2013

  • Nielsen, Jens; d’Avezac, Mayeul; Hetherington, James
  • The Journal of Chemical Physics, Vol. 139, Issue 22
  • DOI: 10.1063/1.4840395

Solving the chemical master equation for monomolecular reaction systems analytically
journal, September 2006


A local superbasin kinetic Monte Carlo method
journal, April 2013

  • Fichthorn, Kristen A.; Lin, Yangzheng
  • The Journal of Chemical Physics, Vol. 138, Issue 16
  • DOI: 10.1063/1.4801869

On the importance of metal–oxide interface sites for the water–gas shift reaction over Pt/CeO2 catalysts
journal, January 2014


Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems
journal, May 2005

  • Goutsias, John
  • The Journal of Chemical Physics, Vol. 122, Issue 18
  • DOI: 10.1063/1.1889434

Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling
journal, February 2016

  • Sutton, Jonathan E.; Guo, Wei; Katsoulakis, Markos A.
  • Nature Chemistry, Vol. 8, Issue 4
  • DOI: 10.1038/nchem.2454

Likelihood ratio gradient estimation for stochastic systems
journal, October 1990


Degree of rate control approach to computational catalyst screening
journal, October 2015


An overview of spatial microscopic and accelerated kinetic Monte Carlo methods
journal, February 2007

  • Chatterjee, Abhijit; Vlachos, Dionisios G.
  • Journal of Computer-Aided Materials Design, Vol. 14, Issue 2
  • DOI: 10.1007/s10820-006-9042-9

Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
journal, January 2007

  • E., Weinan; Liu, Di; Vanden-Eijnden, Eric
  • Journal of Computational Physics, Vol. 221, Issue 1
  • DOI: 10.1016/j.jcp.2006.06.019

Efficient gradient estimation using finite differencing and likelihood ratios for kinetic Monte Carlo simulations
journal, August 2012

  • McGill, Jacob A.; Ogunnaike, Babatunde A.; Vlachos, Dionisios G.
  • Journal of Computational Physics, Vol. 231, Issue 21
  • DOI: 10.1016/j.jcp.2012.06.037

Generalized Temporal Acceleration Scheme for Kinetic Monte Carlo Simulations of Surface Catalytic Processes by Scaling the Rates of Fast Reactions
journal, March 2017

  • Dybeck, Eric C.; Plaisance, Craig P.; Neurock, Matthew
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 4
  • DOI: 10.1021/acs.jctc.6b00859

Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
journal, March 2003

  • Rao, Christopher V.; Arkin, Adam P.
  • The Journal of Chemical Physics, Vol. 118, Issue 11
  • DOI: 10.1063/1.1545446

Control of Metal Nanocrystal Size Reveals Metal-Support Interface Role for Ceria Catalysts
journal, July 2013


Unraveling the Complexity of Catalytic Reactions via Kinetic Monte Carlo Simulation: Current Status and Frontiers
journal, November 2012

  • Stamatakis, Michail; Vlachos, Dionisios G.
  • ACS Catalysis, Vol. 2, Issue 12
  • DOI: 10.1021/cs3005709

Finding the Rate-Determining Step in a Mechanism
journal, December 2001


CO Oxidation on Pd(111): A First-Principles-Based Kinetic Monte Carlo Study
journal, May 2014

  • Piccinin, Simone; Stamatakis, Michail
  • ACS Catalysis, Vol. 4, Issue 7
  • DOI: 10.1021/cs500377j

Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
journal, October 2002

  • Haseltine, Eric L.; Rawlings, James B.
  • The Journal of Chemical Physics, Vol. 117, Issue 15
  • DOI: 10.1063/1.1505860

The chemical Langevin equation
journal, July 2000

  • Gillespie, Daniel T.
  • The Journal of Chemical Physics, Vol. 113, Issue 1
  • DOI: 10.1063/1.481811

Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems
journal, July 2005

  • Cao, Yang; Gillespie, Dan; Petzold, Linda
  • Journal of Computational Physics, Vol. 206, Issue 2
  • DOI: 10.1016/j.jcp.2004.12.014

Binomial distribution based τ-leap accelerated stochastic simulation
journal, January 2005

  • Chatterjee, Abhijit; Vlachos, Dionisios G.; Katsoulakis, Markos A.
  • The Journal of Chemical Physics, Vol. 122, Issue 2
  • DOI: 10.1063/1.1833357

The water-gas shift reaction on Pt/γ-Al2O3 catalyst: Operando SSITKA-DRIFTS-mass spectroscopy studies
journal, November 2008

  • Kalamaras, Christos M.; Olympiou, George G.; Efstathiou, Angelos M.
  • Catalysis Today, Vol. 138, Issue 3-4
  • DOI: 10.1016/j.cattod.2008.06.010

Is the water–gas shift reaction on Pt simple?
journal, July 2005


Comparison of finite difference based methods to obtain sensitivities of stochastic chemical kinetic models
journal, February 2013

  • Srivastava, Rishi; Anderson, David F.; Rawlings, James B.
  • The Journal of Chemical Physics, Vol. 138, Issue 7
  • DOI: 10.1063/1.4790650

First-Principles-Based Kinetic Monte Carlo Simulation of the Structure Sensitivity of the Water–Gas Shift Reaction on Platinum Surfaces
journal, November 2011

  • Stamatakis, Michail; Chen, Ying; Vlachos, Dionisios G.
  • The Journal of Physical Chemistry C, Vol. 115, Issue 50
  • DOI: 10.1021/jp2071869

Multiscale Modeling Reveals Poisoning Mechanisms of MgO-Supported Au Clusters in CO Oxidation
journal, June 2012

  • Stamatakis, Michail; Christiansen, Matthew A.; Vlachos, Dionisios G.
  • Nano Letters, Vol. 12, Issue 7
  • DOI: 10.1021/nl301318b

Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm
journal, October 2005

  • Samant, A.; Vlachos, D. G.
  • The Journal of Chemical Physics, Vol. 123, Issue 14
  • DOI: 10.1063/1.2046628

Design Principles of Heteroepitaxial Bimetallic Catalysts
journal, September 2013

  • Guo, Wei; Stamatakis, Michail; Vlachos, Dionisios G.
  • ACS Catalysis, Vol. 3, Issue 10
  • DOI: 10.1021/cs4005166

Net-event kinetic Monte Carlo for overcoming stiffness in spatially homogeneous and distributed systems
journal, March 2005


Efficient step size selection for the tau-leaping simulation method
journal, January 2006

  • Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 124, Issue 4
  • DOI: 10.1063/1.2159468

Does phenomenological kinetics provide an adequate description of heterogeneous catalytic reactions?
journal, May 2007

  • Temel, Burcin; Meskine, Hakim; Reuter, Karsten
  • The Journal of Chemical Physics, Vol. 126, Issue 20
  • DOI: 10.1063/1.2741556

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains
journal, January 2012

  • Anderson, David F.
  • SIAM Journal on Numerical Analysis, Vol. 50, Issue 5
  • DOI: 10.1137/110849079

Influence of Step Defects on Methanol Decomposition: Periodic Density Functional Studies on Pd(211) and Kinetic Monte Carlo Simulations
journal, December 2012

  • Lin, Sen; Ma, Jianyi; Zhou, Linsen
  • The Journal of Physical Chemistry C, Vol. 117, Issue 1
  • DOI: 10.1021/jp310600q

A review of multiscale modeling of metal-catalyzed reactions: Mechanism development for complexity and emergent behavior
journal, October 2011

  • Salciccioli, M.; Stamatakis, M.; Caratzoulas, S.
  • Chemical Engineering Science, Vol. 66, Issue 19
  • DOI: 10.1016/j.ces.2011.05.050

Patched bimetallic surfaces are active catalysts for ammonia decomposition
journal, October 2015

  • Guo, Wei; Vlachos, Dionisios G.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms9619

Examination of the concept of degree of rate control by first-principles kinetic Monte Carlo simulations
journal, June 2009


Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions
journal, February 2005

  • Salis, Howard; Kaznessis, Yiannis
  • The Journal of Chemical Physics, Vol. 122, Issue 5
  • DOI: 10.1063/1.1835951

Optimisation of simulations of stochastic processes by removal of opposing reactions
journal, February 2016

  • Spill, Fabian; Maini, Philip K.; Byrne, Helen M.
  • The Journal of Chemical Physics, Vol. 144, Issue 8
  • DOI: 10.1063/1.4942413

A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis
journal, January 2017

  • Hoffmann, Max J.; Engelmann, Felix; Matera, Sebastian
  • The Journal of Chemical Physics, Vol. 146, Issue 4
  • DOI: 10.1063/1.4974261

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics
journal, March 2016

  • Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc
  • The Journal of Chemical Physics, Vol. 144, Issue 10
  • DOI: 10.1063/1.4943388

Accurate acceleration of kinetic Monte Carlo simulations through the modification of rate constants
journal, May 2010

  • Chatterjee, Abhijit; Voter, Arthur F.
  • The Journal of Chemical Physics, Vol. 132, Issue 19
  • DOI: 10.1063/1.3409606

Degree of Rate Control: How Much the Energies of Intermediates and Transition States Control Rates
journal, June 2009

  • Stegelmann, Carsten; Andreasen, Anders; Campbell, Charles T.
  • Journal of the American Chemical Society, Vol. 131, Issue 23
  • DOI: 10.1021/ja9000097