Székely Tamás, Burrage Kevin, Zygalakis Konstantinos C, Barrio Manuel
Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK.
BMC Syst Biol. 2014 Jun 18;8:71. doi: 10.1186/1752-0509-8-71.
Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities.
In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie's stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments.
The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.
对于组件数量相对较少的生化系统，必须进行随机模拟以捕捉其固有的噪声。尽管最近在离散随机求解器方面已经开展了大量工作，但仍然需要既快速又准确的数值方法。布利尔施 - 斯托尔方法是一种用于求解常微分方程的既定方法，具备这两种特性。
在本文中，我们提出了随机布利尔施 - 斯托尔方法，这是一种受确定性对应方法启发的用于模拟离散化学反应系统的新数值方法。由于它基于具有高确定性阶数的方法，允许采用更大的步长并实现快速模拟，所以能够实现出色的效率。我们在多个示例问题上把它与欧拉τ跳跃方法以及另外两种较新的τ跳跃方法进行了比较，发现我们的方法不仅非常准确，而且在本文所考虑的所有方法中，就效率而言是最稳健的。它最适合的问题是那些种群数量增加，使用吉莱斯皮随机模拟算法模拟会过于缓慢的问题。对于此类问题，它在矩方面可能实现更高的弱阶数。
随机布利尔施 - 斯托尔方法是一种新型随机求解器，可用于快速且准确的模拟。至关重要的是，与其他类似方法相比，当时间步长增加时，它能更好地保持其高精度。因此，随机布利尔施 - 斯托尔方法既具有计算效率又稳健。这些是任何随机数值方法的关键特性，因为它们通常必须运行数千次模拟。
