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ADM-CLE Approach for Detecting Slow Variables in Continuous Time Markov Chains and Dynamic Data

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  • Title:
    ADM-CLE Approach for Detecting Slow Variables in Continuous Time Markov Chains and Dynamic Data
  • Author: Cucuringu, Mihai ; Erban, Radek
  • Subjects: ADM(ANISOTROPIC DIFFUSION MAP) ; CHEMICAL REACTION NETWORKS ; CHEMICAL REACTIONS ; DIFFUSION MAPS ; Operations Research ; Physical Chemistry ; SLOW VARIABLES ; STATIONARY DISTRIBUTIONS ; Statistics and Probability ; STOCHASTIC CHEMICAL REACTION NETWORKS ; STOCHASTIC PROCESSES ; VARIABLES
  • Description: A method for detecting intrinsic slow variables in high-dimensional stochastic chemical reaction networks is developed and analyzed. It combines anisotropic diffusion maps (ADM)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. Prepared in cooperation with Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, NJ and Mathematical Institute, University of Oxford, Oxford, United Kingdom.
  • Creation Date: 2015
  • Language: English
  • Source: DTIC Technical Reports
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