Stochastic projective methods for simulating stiff chemical reacting systems

Lu, Haokai

doi:10.1016/j.cpc.2012.02.018

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…Another important class of -leap extensions are those that deal with stiff systems [42,57]. In stiff systems, very fast reactions coexist with very slow reactions, where reaction speeds can differ sometimes by several orders of magnitude.…”

Section: Approximate Algorithmsmentioning

confidence: 99%

“…The implicit -leaping method [57] deals with stiff systems by extending the implicit Euler method (used to integrate stiff ODEs) to the stochastic simulation domain. More recently, the so-called stochastic projective methods have been proposed [42], also extending upon corresponding ODE methods, with the aim of improving calculation efficiency by including a number of extrapolation steps in between leaps.…”

Section: Approximate Algorithmsmentioning

confidence: 99%

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Artificial Chemistries on GPU

Yamamoto

Collet

Banzhaf

2013

Natural Computing Series

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An Artificial Chemistry is an abstract model of a chemistry that can be used to model real chemical and biological processes, as well as any natural or artificial phenomena involving interactions among objects and their transformations. It can also be used to perform computations inspired by chemistry, including heuristic optimization algorithms akin to evolutionary algorithms, among other usages. Artificial chemistries are conceptually parallel computations, and could greatly benefit from parallel computer architectures for their simulation, especially as GPU hardware becomes widespread and affordable. However, in practice it is difficult to parallelize artificial chemistry algorithms efficiently for GPUs, particularly in the case of stochastic simulation algorithms that model individual molecular collisions and take chemical kinetics into account. This chapter surveys the current state of the art in the techniques for parallelizing artificial chemistries on GPUs, with focus on their stochastic simulation and their applications in the evolutionary computation domain. Since this problem is far from being entirely solved to satisfaction, some suggestions for future research are also outlined.

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Section: Approximate Algorithmsmentioning

confidence: 99%

Section: Approximate Algorithmsmentioning

confidence: 99%

Artificial Chemistries on GPU

Yamamoto

Collet

Banzhaf

2013

Natural Computing Series

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“…Approaches which do not require explicit separation of scales have also been proposed. For example, interlacing [22,35] and projective [36] strategies were used to restore the overly damped stochastic fluctuations by interchanging large implicit steps with short explicit bursts. Split-step methods have also been proposed for the numerical integration of stiff stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

Slow-scale split-step tau-leap method for stiff stochastic chemical systems

Reshniak

Voss

2019

Journal of Computational and Applied Mathematics

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Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. A motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided, and the obtained results confirm the efficiency of the considered splitting approach.

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“…Several approaches to speeding up the simulation of rare events in stochastic chemical kinetic systems exist. A variety of "leaping" methods can, by taking advantage of approximate time-scale separation, accelerate the SSA itself [21][22][23][24][25][26][27][28]. Kuwahara and Mura's weighted stochastic simulation (wSSA) method [29] was refined by Gillespie and Petzold et al [30][31][32][33], and is based on importance sampling.…”

Section: Introductionmentioning

confidence: 99%

Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories

Donovan

Sedgewick

Faeder

et al. 2013

The Journal of Chemical Physics

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We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study, WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent "brute-force" calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over "brute-force" in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ~10(12) to ~10(18) for characterizing rare states in a distribution, and ~10(2) to ~10(4) for finding mean first passage times.

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Stochastic projective methods for simulating stiff chemical reacting systems

Cited by 9 publications

References 15 publications

Artificial Chemistries on GPU

Artificial Chemistries on GPU

Slow-scale split-step tau-leap method for stiff stochastic chemical systems

Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories

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