Hybrid discrete/continuum algorithms for stochastic reaction networks
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum FokkerPlanck equation. The FokkerPlanck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a twospecies circadian model with computational efficiency gains of about one order of magnitude.
 Authors:

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 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Publication Date:
 Report Number(s):
 SAND201310187J
Journal ID: ISSN 00219991; 485627
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 281; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Chemical Master Equation; Fokker–Planck equation; finite volume; Flux splitting; hybrid discretecontinuum models
 OSTI Identifier:
 1121280
 Alternate Identifier(s):
 OSTI ID: 1246992
Safta, Cosmin, Sargsyan, Khachik, Debusschere, Bert, and Najm, Habib N. Hybrid discrete/continuum algorithms for stochastic reaction networks. United States: N. p.,
Web. doi:10.1016/j.jcp.2014.10.026.
Safta, Cosmin, Sargsyan, Khachik, Debusschere, Bert, & Najm, Habib N. Hybrid discrete/continuum algorithms for stochastic reaction networks. United States. doi:10.1016/j.jcp.2014.10.026.
Safta, Cosmin, Sargsyan, Khachik, Debusschere, Bert, and Najm, Habib N. 2014.
"Hybrid discrete/continuum algorithms for stochastic reaction networks". United States.
doi:10.1016/j.jcp.2014.10.026. https://www.osti.gov/servlets/purl/1121280.
@article{osti_1121280,
title = {Hybrid discrete/continuum algorithms for stochastic reaction networks},
author = {Safta, Cosmin and Sargsyan, Khachik and Debusschere, Bert and Najm, Habib N.},
abstractNote = {Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum FokkerPlanck equation. The FokkerPlanck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a twospecies circadian model with computational efficiency gains of about one order of magnitude.},
doi = {10.1016/j.jcp.2014.10.026},
journal = {Journal of Computational Physics},
number = C,
volume = 281,
place = {United States},
year = {2014},
month = {10}
}