An analyzable method for constructing a cellular automaton from a continuous system
An analyzable method for constructing a cellular automaton from a continuous system
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一种从连续系统构造元胞自动机的可分析方法
DOI：
10.1109/candar.2015.111
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
and Naoto Nakano
中科院分区：
文献类型：
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作者：
Akane Kawaharada;Tomoyuki Miyaji;and Naoto Nakano
提出了一种构造模拟偏微分方程的元胞自动机的可分析方法。我们遵循Kawaharada和Iima的研究，他们提出了一个从给定数据集实证构建CA的过程。原则上，他们的程序适用于任何时空数据集，包括PDE的数值解。然而，所得到的CA很难被识别的先验理论的方式。我们提出的一个优点是，它是能够进行数学分析。关键是设计一组最小的数值实验，用于收集时空数据集，以供在此过程中使用。我们将所提出的方法应用于三个偏微分方程的数值解：扩散方程，对流方程和Burgers方程。我们讨论的差异与现有的方法和渐近收敛的局部规则依赖于数据量，利用所提出的方法的优点。
We propose an analyzable method of constructing a cellular automaton (CA) which simulates a given partial differential equation (PDE). We follow the study by Kawaharada and Iima who proposed a procedure for empirical construction of a CA from a given dataset. Their procedure is applicable for any spatiotemporal dataset, including numerical solutions of a PDE, in principle. However, the resultant CA is hardly identified a priori in a theoretical manner. An advantage of our proposed is that it is capable of being analyzed mathematically. The key is to design a minimal set of numerical experiments for collecting the spatiotemporal dataset for use in this procedure. We apply the proposed method to numerical solutions of three PDEs: the diffusion equation, the advection equation, and the Burgers equation. We discuss the difference with the existing method and the asymptotic convergence of the local rule depending on the amount of data, exploiting the advantage of the proposed method.