Arun R, Sathish Aravindh M, Venkatesan A, Lakshmanan M
Department of Nonlinear Dynamics, School of Physics, <a href="https://ror.org/02w7vnb60">Bharathidasan University</a>, Tiruchirappalli - 620 024, India.
Department of Aerospace, Indian Institute of Technology Madras, Chennai 600 036, India.
Phys Rev E. 2024 Sep;110(3-1):034204. doi: 10.1103/PhysRevE.110.034204.
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).
近期关于储层计算的研究主要涉及一个高维动力系统作为储层，该系统将输入转换并存储为用于时间和非时间数据处理的高维状态。我们在此展示一种方法，通过使用非线性映射（即逻辑斯谛映射）和简单的有限三角级数构建虚拟节点作为储层计算中的储层，来预测时间和非时间任务。我们以高精度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 - 罗斯系统用于时间任务，以及一个七阶多项式用于非时间任务。此外，在存在噪声的情况下进行预测，发现与目标值非常吻合。值得注意的是，逻辑斯谛映射表现良好，预测值接近实际值或目标值。均方根误差的低值证实了该方法在效率方面的准确性。我们的方法消除了在储层计算中构建储层时对连续动力系统的需求。此外，对三个不同非线性系统的准确预测表明该方法可被视为一种通用方法，可应用于预测许多系统。最后，我们表明该方法还能准确预测罗斯勒系统未来所有三个变量的时间序列（自预测）。
