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Title: Hybrid discrete/continuum algorithms for stochastic reaction networks

Abstract

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 Fokker-Planck equation. The Fokker-Planck 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 two-species circadian model with computational efficiency gains of about one order of magnitude.

Authors:
 [1];  [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1121280
Alternate Identifier(s):
OSTI ID: 1246992
Report Number(s):
SAND-2013-10187J
Journal ID: ISSN 0021-9991; 485627
Grant/Contract Number:  
AC04-94AL85000; 07-012783
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 281; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Chemical Master Equation; Fokker–Planck equation; finite volume; Flux splitting; hybrid discrete-continuum models

Citation Formats

Safta, Cosmin, Sargsyan, Khachik, Debusschere, Bert, and Najm, Habib N. Hybrid discrete/continuum algorithms for stochastic reaction networks. United States: N. p., 2014. 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. https://doi.org/10.1016/j.jcp.2014.10.026
Safta, Cosmin, Sargsyan, Khachik, Debusschere, Bert, and Najm, Habib N. Wed . "Hybrid discrete/continuum algorithms for stochastic reaction networks". United States. https://doi.org/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 Fokker-Planck equation. The Fokker-Planck 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 two-species 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 = {Wed Oct 22 00:00:00 EDT 2014},
month = {Wed Oct 22 00:00:00 EDT 2014}
}

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Cited by: 11 works
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