skip to main content


Title: 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 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.
 [1] ;  [1] ; ORCiD logo [1] ; ORCiD logo [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0021-9991; 485627
Grant/Contract Number:
AC04-94AL85000; 07-012783
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 281; Journal Issue: C; Journal ID: ISSN 0021-9991
Research Org:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Chemical Master Equation; Fokker–Planck equation; finite volume; Flux splitting; hybrid discrete-continuum models
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1246992