利用逻辑地图进行水库计算

IF 2.4 3区 物理与天体物理 Q1 Mathematics
R. Arun, M. Sathish Aravindh, A. Venkatesan, M. Lakshmanan
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引用次数: 0

摘要

最近关于蓄水池计算的研究主要涉及一个高维动态系统作为蓄水池,它将输入转换并存储为更高维的状态,用于时态和非时态数据处理。我们在此展示了一种预测时空任务的方法,即利用非线性映射(即逻辑映射)和简单的有限三角级数,通过构建虚拟节点来构成水库计算中的水库。我们为时间任务预测了三个非线性系统,即洛伦兹系统、罗斯勒系统和辛德马什-罗斯系统,并为非时间任务预测了一个七阶多项式,预测结果非常准确。此外,在有噪声的情况下也能进行预测,并发现预测结果与目标非常吻合。值得注意的是,逻辑图表现出色,预测值接近实际值或目标值。较低的均方根误差值证实了这种方法在效率方面的准确性。我们的方法消除了储层计算中构建储层的连续动力系统的必要性。此外,对三种不同非线性系统的精确预测表明,这种方法可被视为一种通用方法,可用于预测许多系统。最后,我们证明了该方法还能准确预测罗斯勒系统所有三个变量的未来时间序列(自我预测)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Reservoir computing with logistic map

Reservoir computing with logistic map
Recent studies on reservoir computing essentially involve a high-dimensional dynamical system as the reservoir, which transforms and stores the input as a higher-dimensional state for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, and Hindmarsh-Rose, for temporal tasks and a seventh-order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rössler system for the future (self-prediction).
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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