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

Cucuringu, Mihai; Erban, Radek

doi:10.1137/15m1017120

Cited by 3 publications

(1 citation statement)

References 46 publications

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“…One can use either short bursts of the Gillespie SSA on a range of points on the slow state space to approximate the effective drift and diffusion of the slow variable [12] or the constrained multiscale algorithm (CMA) [5], which utilizes a modified SSA that constrains the trajectories it computes to a particular point on the slow state space. These algorithms can be further extended to automatic detection of slow variables [10,26,6], but in this paper we assume that the division of state space into slow and fast variables is a priori known and fixed during the whole simulation.…”

Section: B145mentioning

confidence: 99%

Error Analysis of Diffusion Approximation Methods for Multiscale Systems in Reaction Kinetics

Cotter

Erban²

2016

SIAM J. Sci. Comput.

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Abstract. Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation approximation of the paths. In this paper, multiscale methods for approximating paths are used to formulate different strategies for estimating the dynamics by diffusion processes. We then analyze how efficient and accurate these methods are in a range of different scenarios and compare their respective advantages and disadvantages to other methods proposed to analyze multiscale chemical networks.

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Section: B145mentioning

confidence: 99%

Error Analysis of Diffusion Approximation Methods for Multiscale Systems in Reaction Kinetics

Cotter

Erban²

2016

SIAM J. Sci. Comput.

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Multiscale Stochastic Reaction–Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations

Kang

Erban

2019

Bull Math Biol

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Two multiscale algorithms for stochastic simulations of reaction–diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction–diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches.

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Explicit time integration of the stiff chemical Langevin equations using computational singular perturbation

Han

Valorani

Najm

2019

The Journal of Chemical Physics

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A stable explicit time-scale splitting algorithm for stiff chemical Langevin equations (CLEs) is developed, based on the concept of computational singular perturbation. The drift term of the CLE is projected onto basis vectors that span the fast and slow subdomains. The corresponding fast modes exhaust quickly, in the mean sense, and the system state then evolves, with a mean drift controlled by slow modes, on a random manifold. The drift-driven time evolution of the state due to fast exhausted modes is modeled algebraically as an exponential decay process, while that due to slow drift modes and diffusional processes is integrated explicitly. This allows time integration step sizes much larger than those required by typical explicit numerical methods for stiff stochastic differential equations. The algorithm is motivated and discussed, and extensive numerical experiments are conducted to illustrate its accuracy and stability with a number of model systems.

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

Cited by 3 publications

References 46 publications

Error Analysis of Diffusion Approximation Methods for Multiscale Systems in Reaction Kinetics

Error Analysis of Diffusion Approximation Methods for Multiscale Systems in Reaction Kinetics

Multiscale Stochastic Reaction–Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations

Explicit time integration of the stiff chemical Langevin equations using computational singular perturbation

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