Kinetic Monte Carlo (KMC) methods have been a successful technique for accelerating time scales and increasing system sizes beyond those achievable with fully atomistic simulations. However, a requirement for its success is a priori knowledge of all relevant reaction pathways and their rate coefficients. This can be difficult for systems with complex chemistry, such as shock-compressed materials at high temperatures and pressures or phenolic spacecraft heat shields undergoing pyrolysis, which can consist of hundreds of molecular species and thousands of distinct reactions. In this work, we develop a method for first estimating a KMC model composed of elementary reactions and rate coefficients by using large datasets derived from a few molecular dynamics (MD) simulations of shock compressed liquid methane, and then using L1 regularization to reduce the estimated chemical reaction network. We find that the full network of 2613 reactions can be reduced by 89% while incurring approximately 9% error in the dominant species (CH4) population. We find that the degree of sparsity achievable decreases when similar accuracy is required for additional populations of species.
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L. Wasserman, All of Statistics: A Concise Course in Statistical Inference. (Springer, New York, 2004) p. 122–128.
L. Petzold and W. Zhu, AIChE J. 45: 869–886 (1999).
R. Hannemann-Tamás, A. Gábor, G. Szederkényi, K. Hangos, Computers & Mathematics with Applications 65, 10 (2013).
N. Sikalo, O. Hasemann, C. Schulz, A. Kempf, I. Wlokas, Intl J. of Chem. Kinetics 46, 1 (2014).
T. Nagy and T. Turányi, Combustion and Flame 156, 2 (2009).
K. Chenoweth, A. C. T. van Duin, W. A. Goddard, III, J. Phys. Chem. A 112, 5 (2008).
T. Qi, E. J. Reed, J. Phys. Chem. A 116, 42 (2012).
D. Gillespie, J. Comput. Phys. 22, 4 (1976).
D. Gillespie, J. Chem. Phys. 115, 4 (2001).
D. Gillespie, J. Chem. Phys. 113, 1 (2000).
R. Tibshirani, J. R. Stat. Soc. B 58, 1 (1996).
M. R. Osborne , B. Presnell, B. A. Turlach, J. Comp. Graph. Stat. 9, 2 (2000).
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx, September 2013.
M. Grant and S. Boyd, in Recent Advances in Learning and Control, edited by V. Blondel, S. Boyd, H. Kimura (Springer, New York 2008), p. 95–110.
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Yang, Q., Sing-Long, C.A. & Reed, E.J. L1 Regularization-Based Model Reduction of Complex Chemistry Molecular Dynamics for Statistical Learning of Kinetic Monte Carlo Models. MRS Advances 1, 1767–1772 (2016). https://doi.org/10.1557/adv.2016.124