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Data-based prediction and causality inference of nonlinear dynamics

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Abstract

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which cannot only recover nonlinear behaviors but also predict future dynamics. Due to the advances of modern technology, big data becomes increasingly accessible and consequently the problem of reconstructing systems from measured data or time series plays a central role in many scientic disciplines. In recent decades, nonlinear methods rooted in state space reconstruction have been developed, and they do not assume any model equations but can recover the dynamics purely from the measured time series data. In this review, the development of state space reconstruction techniques will be introduced and the recent advances in systems prediction and causality inference using state space reconstruction will be presented. Particularly, the cutting-edge method to deal with short-term time series data will be focused on. Finally, the advantages as well as the remaining problems in this field are discussed.

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFA0505500), Japan Society for the Promotion of Science KAKENHI Program (Grant No. JP15H05707), and National Natural Science Foundation of China (Grant Nos. 11771010, 31771476, 91530320, 91529303, 91439103 and 81471047).

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  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, China

    Huanfei Ma

  2. Institute of Industrial Science, The University of Tokyo, Tokyo, 153-8505, Japan

    Siyang Leng & Luonan Chen

  3. Key Laboratory of Systems Biology, Innovation Center for Cell Signaling Network, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai, 200031, China

    Luonan Chen

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Ma, H., Leng, S. & Chen, L. Data-based prediction and causality inference of nonlinear dynamics. Sci. China Math. 61, 403–420 (2018). https://doi.org/10.1007/s11425-017-9177-0

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