Optimisation of simulations of stochastic processes by removal of opposing reactions,The Journal of Chemical Physics

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Optimisation of simulations of stochastic processes by removal of opposing reactions
The Journal of Chemical Physics ( IF 3.1 ) Pub Date : 2016-02-24 16:18:54 , DOI: 10.1063/1.4942413
Fabian Spill _{1,

2} , Philip K. Maini ₃ , Helen M. Byrne ₃

Affiliation

Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a large number of algorithms have been developed to speed up simulations. However, a drawback of many of these algorithms is that their implementation is more complicated than, for instance, the Gillespie algorithm, which is widely used to simulate the chemical master equation, and can be implemented with a few lines of code. Here, we present an algorithm which does not modify the way in which the master equation is solved, but instead modifies the transition rates. It works for all models in which reversible reactions occur by replacing such reversible reactions with effective net reactions. Examples of such systems include reaction-diffusion systems, in which diffusion is modelled by a random walk. The random movement of particles between neighbouring sites is then replaced with a net random flux. Furthermore, as we modify the transition rates of the model, rather than its implementation on a computer, our method can be combined with existing algorithms that were designed to speed up simulations of the stochastic master equation. By focusing on some specific models, we show how our algorithm can significantly speed up model simulations while maintaining essential features of the original model.

中文翻译：

通过消除相反的反应来优化随机过程的模拟

调用化学主方程的模型已在许多科学领域中使用，因此，许多研究人员都对它们进行仿真。问题的复杂性通常需要相当大的计算能力，因此已经开发了大量算法来加快仿真速度。但是，这些算法中的许多算法的缺点是，它们的实现比例如Gillespie算法要复杂得多，Gillespie算法被广泛用于模拟化学主方程，并且可以用几行代码来实现。在这里，我们提出一种算法，该算法不会修改求解主方程的方式，而是会修改过渡速率。通过用有效的净反应替换可逆反应，该方法适用于所有发生可逆反应的模型。这种系统的例子包括反应扩散系统，其中扩散是通过随机游走来建模的。然后，用净随机通量代替相邻位置之间的粒子随机运动。此外，随着我们修改模型的转化率，而不是在计算机上实现，我们的方法可以与现有算法相结合，这些算法旨在加快随机主方程的仿真速度。通过关注一些特定模型，我们展示了我们的算法如何在保持原始模型的基本特征的同时，显着加快模型仿真的速度。当我们修改模型的转化率时，而不是在计算机上实现时，我们的方法可以与现有算法结合使用，这些算法旨在加快随机主方程的仿真速度。通过关注一些特定模型，我们展示了我们的算法如何在保持原始模型的基本特征的同时，显着加快模型仿真的速度。当我们修改模型的转化率时，而不是在计算机上实现时，我们的方法可以与现有算法结合使用，这些算法旨在加快随机主方程的仿真速度。通过关注一些特定模型，我们展示了我们的算法如何在保持原始模型的基本特征的同时，显着加快模型仿真的速度。

更新日期：2016-02-25

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