Constrained approximation of effective generators for multiscale stochastic reaction networks and application to conditioned path sampling
Constrained approximation of effective generators for multiscale stochastic reaction networks and application to conditioned path sampling
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DOI：
10.1016/j.jcp.2016.07.035
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发表时间：
2016-10-15
影响因子：
4.1
通讯作者：
Cotter, Simon L.
中科院分区：
文献类型：
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作者：
Cotter, Simon L.
化学动力学多尺度随机系统的有效分析和模拟是一个正在进行的研究领域，也是许多理论和计算挑战的根源。在本文中，我们提出了对约束方法的重大改进，这是一种计算这些系统中缓慢变化量的有效动态的方法，但不依赖于准稳态假设（QSSA）。对于“快”变量和“慢”变量之间的时间尺度差异不太明显的系统，QSSA 可能会导致有效动态估计出现错误。约束方法的这种新应用使我们能够计算慢变量的有效生成器，而无需昂贵的随机模拟。这是通过找到约束系统的生成元的零空间来实现的。对于不可能做到这一点的复杂系统，或者约束子系统本身是多尺度的，可以迭代地应用约束方法。这导致将问题分解为寻找许多小特征值问题的解决方案，这些问题可以使用标准方法有效地解决。由于该方法不依赖于准稳态假设，因此近似的有效动力学非常准确，并且在仅具有单分子反应的系统的情况下是精确的。我们将用一些数字来证明这一点，并使用有效的生成器对以其端点为条件的慢变量的路径进行采样，这对于整个系统的生成器来说在计算上是困难的。 (C) 2016 作者。由爱思唯尔公司出版
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement to the constrained approach, which is a method for computing effective dynamics of slowly changing quantities in these systems, but which does not rely on the quasi-steady-state assumption (QSSA). The QSSA can cause errors in the estimation of effective dynamics for systems where the difference in timescales between the "fast" and "slow" variables is not so pronounced.This new application of the constrained approach allows us to compute the effective generator of the slow variables, without the need for expensive stochastic simulations. This is achieved by finding the null space of the generator of the constrained system. For complex systems where this is not possible, or where the constrained subsystem is itself multiscale, the constrained approach can then be applied iteratively. This results in breaking the problem down into finding the solutions to many small eigenvalue problems, which can be efficiently solved using standard methods.Since this methodology does not rely on the quasi steady-state assumption, the effective dynamics that are approximated are highly accurate, and in the case of systems with only monomolecular reactions, are exact. We will demonstrate this with some numerics, and also use the effective generators to sample paths of the slow variables which are conditioned on their endpoints, a task which would be computationally intractable for the generator of the full system. (C) 2016 The Author. Published by Elsevier Inc.