An adaptive solution to the chemical master equation using quantized tensor trains with sliding windows
An adaptive solution to the chemical master equation using quantized tensor trains with sliding windows
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DOI：
10.1088/1478-3975/aba1d2
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发表时间：
2020-11-01
期刊：
影响因子：
2
通讯作者：
Sidje, Roger B.
中科院分区：
文献类型：
--
作者：
Dinh, Trang;Sidje, Roger B.
在求解生物学问题中的化学主方程时，为了科普极大甚至无限的状态空间，一种有效的策略是将转移矩阵和概率向量限制为有限状态投影（FSP），并以量化张量序列（QTT）格式表示，从而在保持精度的同时节省存储空间。在早期的自适应FSP-QTT算法中，多维状态空间被缩小并保持在超矩形的形式，当需要时，通过选择性地将其一些侧维度加倍来更新该超矩形。然而，这可能导致比必要的状态空间大得多的状态空间，从而妨碍执行时间和步进方案。在这项工作中，我们通过启用可以动态滑动、缩小或扩大的滑动窗口来改进算法，并由许多随机模拟算法轨迹驱动更新。随后的状态空间是一个大大减少超矩形只包含在每个时间步的最可能的状态。三个不同难度的数值实验进行比较，我们的方法与原来的自适应FSP-QTT算法。
To cope with an extremely large or even infinite state space when solving the chemical master equation in biological problems, a potent strategy is to restrict to a finite state projection (FSP) and represent the transition matrix and probability vector in quantized tensor train (QTT) format, leading to savings in storage while retaining accuracy. In an earlier adaptive FSP-QTT algorithm, the multidimensional state space was downsized and kept in the form of a hyper rectangle that was updated when needed by selectively doubling some of its side dimensions. However, this could result in a much larger state space than necessary, with the effect of hampering both the execution time and stepping scheme. In this work, we improve the algorithm by enabling sliding windows that can dynamically slide, shrink or expand, with updates driven by a number of stochastic simulation algorithm trajectories. The ensuing state space is a considerably reduced hyper rectangle containing only the most probable states at each time step. Three numerical experiments of varying difficulty are performed to compare our approach with the original adaptive FSP-QTT algorithm.