Predicting chaotic dynamics from incomplete input via reservoir computing with (D+1)-dimension input and output.
Predicting chaotic dynamics from incomplete input via reservoir computing with (D+1)-dimension input and output.
复制标题
通过使用 (D 1) 维输入和输出的储层计算来预测不完整输入的混沌动力学。
作者：
Lufa Shi;Youfang Yan;Hengtong Wang;Shengjun Wang;S. Qu
尽管数据驱动的机器学习方法已经成功地应用于预测复杂的非线性动力学，但基于过去的不完整信息预测未来的进化仍然是一个挑战。广泛采用的水库计算（RC）很难处理这一点，因为它通常需要完整的观察过去。本文提出了一种具有（D+1）维输入输出（I/O）向量的RC方案来解决这一问题，不完整的输入时间序列或系统的动态轨迹，其中某些状态被随机删除。在该方案中，耦合到存储器的I/O向量被改变为（D+1）维，其中前D维存储与常规RC中一样的状态向量，并且附加维是对应的时间间隔。我们已经成功地将这种方法应用于预测Logistic映射和Lorenz，Rössler和Kuramoto-Sivashinsky系统的未来演化，其中输入是缺少数据的动力学轨迹。分析了有效预测时间（VPT）的下降率依赖性。结果表明，当衰减率θ较小时，该方法可以进行较长时间的VPT预测。分析了高θ失效的原因。我们的RC的可预测性是由所涉及的动力系统的复杂性决定的。它们越复杂，就越难预测。观察到混沌吸引子的完美重构。该方案是对RC的一个很好的推广，可以处理具有规则和不规则时间间隔的输入时间序列。它易于使用，因为它不改变传统RC的基本架构。此外，该方法只需将输出向量中的时间间隔改变为期望值，就可以进行多步预测，优于传统RC只能基于完全规则的输入数据进行一步预测的上级方法。
Predicting future evolution based on incomplete information of the past is still a challenge even though data-driven machine learning approaches have been successfully applied to forecast complex nonlinear dynamics. The widely adopted reservoir computing (RC) can hardly deal with this since it usually requires complete observations of the past. In this paper, a scheme of RC with (D+1)-dimension input and output (I/O) vectors is proposed to solve this problem, i.e., the incomplete input time series or dynamical trajectories of a system, in which certain portion of states are randomly removed. In this scheme, the I/O vectors coupled to the reservoir are changed to (D+1)-dimension, where the first D dimensions store the state vector as in the conventional RC, and the additional dimension is the corresponding time interval. We have successfully applied this approach to predict the future evolution of the logistic map and Lorenz, Rössler, and Kuramoto-Sivashinsky systems, where the inputs are the dynamical trajectories with missing data. The dropoff rate dependence of the valid prediction time (VPT) is analyzed. The results show that it can make forecasting with much longer VPT when the dropoff rate θ is lower. The reason for the failure at high θ is analyzed. The predictability of our RC is determined by the complexity of the dynamical systems involved. The more complex they are, the more difficult they are to predict. Perfect reconstructions of chaotic attractors are observed. This scheme is a pretty good generalization to RC and can treat input time series with regular and irregular time intervals. It is easy to use since it does not change the basic architecture of conventional RC. Furthermore, it can make multistep-ahead prediction just by changing the time interval in the output vector into a desired value, which is superior to conventional RC that can only do one-step-ahead forecasting based on complete regular input data.
影响因子：
7.8
作者：
Grigoryeva, Lyudmila;Ortega, Juan-Pablo
通讯作者：
Ortega, Juan-Pablo