Approximate Moment Dynamics for Chemically Reacting Systems
Approximate Moment Dynamics for Chemically Reacting Systems
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DOI：
10.1109/tac.2010.2088631
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发表时间：
2011-02-01
影响因子：
6.8
通讯作者：
Hespanha, Joao P.
中科院分区：
文献类型：
--
作者：
Singh, Abhyudai;Hespanha, Joao P.
在化学动力学的随机公式中，描述所涉及的不同物种的分子数量的低阶统计矩的时间演化的微分方程通常不是封闭的，因为该方程的右侧取决于高阶矩。最近的工作提出了一种基于导数匹配的矩闭合技术，该技术通过将高阶矩近似为低阶矩的非线性函数来闭合矩方程。我们在这里提供了这种矩闭合技术的数学证明，并通过与替代方法的比较来强调其性能。这些比较表明，这种基于导数匹配的矩闭合技术可以提供更准确的矩动态估计，特别是当群体规模较小时。最后，我们表明，所提出的矩闭合方案的准确性可以通过增加额外的计算量来任意提高。
In the stochastic formulation of chemical kinetics, the differential equation that describes the time evolution of the lower-order statistical moments for the number of molecules of the different species involved, is generally not closed, in the sense that the right-hand side of this equation depends on higher-order moments. Recent work has proposed a moment closure technique based on derivative-matching, which closes the moment equations by approximating higher-order moments as nonlinear functions of lower-order moments. We here provide a mathematical proof of this moment closure technique, and highlight its performance through comparisons with alternative methods. These comparisons reveal that this moment closure technique based on derivative-matching provides more accurate estimates of the moment dynamics, especially when the population size is small. Finally, we show that the accuracy of the proposed moment closure scheme can be arbitrarily increased by incurring additional computational effort.