Constructing Cellular Automaton Models from Observation Data

Kawaharada, Akane; Iima, Makoto

doi:10.1109/candar.2013.99

Cited by 6 publications

(4 citation statements)

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“…Burgers' equation is a nonlinear example that possesses both characteristics of advection and diffusion. The previous studies supposed the number of states is less than or equal to eight ( [4], [5], [2], [6], and [3]), and we have used k = 8 in this study, which is far from the limit k → ∞. Nevertheless, a stochastic CA obtained by the minimal method reproduces qualitative feature of the corresponding difference equation in each case.…”

Section: Burgers' Casmentioning

confidence: 95%

“…We recall the experimental method [2]. We consider the initial-boundary value problem of (2.2), (2.5), and (2.8) on a finite interval with the periodic boundary condition.…”

Section: Procedures Of the Experimental Methodsmentioning

confidence: 99%

“…The range of u n i can be arbitrary. In addition, inhomogeneous subintervals can be used to discretize states if needed (See [2]). …”

Section: Procedures Of the Experimental Methodsmentioning

confidence: 99%

“…A method of constructing a cellular automaton (CA) from observation data of laboratory experiments was proposed by Kawaharada and Iima [2]. The essential part of the method is to find local rules of a CA that appear most frequently in spatiotemporal data of an experiment.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a method for constructing a cellular automaton from a continuous system

Kawaharada

Miyaji

Nakano

2016

IJNC

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A method of constructing a cellular automaton (CA) from numerical solutions of a given partial differential equation (PDE) is considered. It consists of two parts, namely, collecting spatiotemporal data numerically and finding local rules of a CA that appear most frequently.In this paper, we analyze the method mathematically to examine its selectivity and its robustness of the derived local rules so that we can ensure validity of the resultant CA model. In particular, we investigated two limit cases: (a) the number of states of CA goes to infinity and (b) the number of spatiotemporal data goes to infinity. In the former case, we prove that the resultant CA converges to the difference equation where numerical solutions of a PDE are collected. In the latter case, through mathematical analysis, we derive conditions that the resultant CA is uniquely determined when the method of constructing a CA is applied to the diffusion equation. Our study can be a theoretical foundation of empirical CA modeling methods to create a reasonable CA which can somehow reproduce the original behavior of datasets under consideration.

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Section: Burgers' Casmentioning

confidence: 95%

“…We recall the experimental method [2]. We consider the initial-boundary value problem of (2.2), (2.5), and (2.8) on a finite interval with the periodic boundary condition.…”

Section: Procedures Of the Experimental Methodsmentioning

confidence: 99%

“…The range of u n i can be arbitrary. In addition, inhomogeneous subintervals can be used to discretize states if needed (See [2]). …”

Section: Procedures Of the Experimental Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations