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 logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely Lorenz, R\"ossler, 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 for the future (self prediction).

翻译：近期关于储层计算的研究主要利用高维动力系统作为储层，通过将输入信号转换为高维状态进行时空与非时序数据处理。本文提出一种利用非线性映射——即逻辑斯蒂映射——与简单有限三角级数构建虚拟节点作为储层计算核心的方法，用于预测时空与非时序任务。我们成功预测了三个非线性系统（洛伦兹系统、罗斯勒系统与欣德马什-罗斯系统）的时序行为，并精确拟合了七阶多项式描述的非时序系统。即使在噪声干扰下，预测结果仍与目标值高度吻合。值得注意的是，逻辑斯蒂映射展现出优异性能，预测值几乎完全逼近实际目标值。低均方根误差验证了该方法在效率上的准确性。本方法消除了在储层计算中构建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该方法具有普适性，可推广至多种系统预测。最后，我们证明了该方法还能准确预测未来时序（自预测）。