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Fractional Order Echo State Network for Time Series Prediction

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Abstract

In this brief, considering the infinite memory of fractional-order differential equation, a fractional-order echo state network (FESN) is given for time series prediction. For the FESN, the reservoir state differential equation is replaced with fractional-order differential equation. According to the advantages of FESN, the dynamic characteristics of a class of time series can be fully reflected. In order to improve the prediction performance of FESN, a fractional-order output weights learning method and a fractional-order parameter optimization method are given to train the output weights and optimize the reservoir parameters, respectively. Finally, two numerical examples are used to show the effectiveness of FESN.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61973070, 61433004, and 61627809, and in part by SAPI Fundamental Research Funds under Grant 2018ZCX22, and in part by the Fundamental Research Funds for the Central Universities under Grant N160406002.

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  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Xianshuang Yao & Zhanshan Wang

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  1. Xianshuang Yao
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  2. Zhanshan Wang
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Correspondence to Zhanshan Wang.

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Yao, X., Wang, Z. Fractional Order Echo State Network for Time Series Prediction. Neural Process Lett 52, 603–614 (2020). https://doi.org/10.1007/s11063-020-10267-y

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