慢尺度分步τ跃方法用于刚性随机化学系统
Slow-scale split-step tau-leap method for stiff stochastic chemical systems
AI总结：
本文提出了一种慢尺度分步τ跃方法，用于高效模拟刚性随机化学系统，通过分裂启发式方法解决刚性系统中数值解的松弛时间过长和协方差不准确的问题，该方法通过估计线性化系统的矩方程中的未知参数，实现了对线性标量测试方程的精确均值和方差的再现，并在非线性系统中验证了其有效性。
摘要：
τ跃是一种用于离散状态连续时间马尔可夫链近似模拟的算法家族。此类方法的发展动机可以归因于化学动力学和系统生物学领域。已知生化系统的动态行为往往本质上是刚性的，这给其数值近似带来了严峻挑战。将刚性确定性求解器直接扩展到随机积分通常会产生数值解，其松弛时间要么不实际，要么协方差不正确。在本文中，我们提出了一种分裂启发式方法，以解决这些问题。所提出的积分器包含若干未知参数，这些参数从相应线性化系统的矩方程中估计得到。我们证明该方法能够再现线性标量测试方程的精确均值和方差，并在至少线性情况下表现出对任意刚性系统的良好精度。还提供了线性和非线性系统的数值示例，所得结果验证了所考虑的分裂方法的有效性。
英文摘要：
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. 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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