ADM-CLE approach for detecting slow variables in continuous time Markov Chains and dynamic data

Mihai Cucuringu, Radek Erban

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A method for detecting intrinsic slow variables in stochastic chemical reaction networks is developed and analyzed. It combines anisotropic diffusion maps (ADMs) with approximations based on the chemical Langevin equation (CLE). The resulting approach, called ADM-CLE, has the potential of being more efficient than the ADM method for a large class of chemical reaction systems, because it replaces the computationally most expensive step of ADM (running local short bursts of simulations) by using an approximation based on the CLE. The ADM-CLE approach can be used to estimate the stationary distribution of the detected slow variable, without any a priori knowledge of it. If the conditional distribution of the fast variables can be obtained analytically, then the resulting ADM-CLE approach does not make any use of Monte Carlo simulations to estimate the distributions of both slow and fast variables.
Original languageEnglish (US)
Pages (from-to)B76-B101
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - Feb 22 2017
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-08
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 239870. It is based on work supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The first author's research was supported by Amit Singer of PACM, by AFOSR MURI grant FA9550-10-1-0569, by award R01GM090200 from the NIGMS, and by award FA9550-09-1-0551 from AFOSR. The second author's research was supported by a University Research Fellowship from the Royal Society, by a Nicholas Kurti Junior Fellowship from Brasenose College, University of Oxford, and by a Philip Leverhulme Prize from the Leverhulme Trust. This prize money was used to support research visits of Mihai Cucuringu in Oxford.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics


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