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Short-term data-based spatial parallel autoreservoir computing on spatiotemporally chaotic system prediction

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Abstract

This paper presents a novel machine learning method for predicting chaotic spatiotemporal systems by proposing a parallel reservoir-like neural network. In contrast to previous machine learning methods, which require big data and suffer from high computing costs, the main advantage of the method is that it is based on short-term data and only needs to train the weight of the output layer. Theoretically, the ratio of training data length and the prediction data length can reach 2:1. First, the method for transforming an infinite-dimensional system into a finite-dimensional system is introduced. Then, based on this concept and the spatiotemporal information transformation, a network training algorithm of spatial parallel autoreservoir computing structure is proposed. Numerical experiments verified that with short-term data, the proposed method performs better than some widely used data-driven methods.

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Code Availability Statement

The code used in this study is available at https://github.com/413582273/SPARNN.

References

  1. Bengio Y, Simard P, Frasconi P (1994) Learning long-term dependencies with gradient descent is difficult. IEEE Trans Neural Netw 5(2):157–166. https://doi.org/10.1109/72.279181

    Article  Google Scholar 

  2. Brenner M, Eldredge J, Freund J (2019) Perspective on machine learning for advancing fluid mechanics. Phys Rev Fluids. https://doi.org/10.1103/PhysRevFluids.4.100501

    Article  Google Scholar 

  3. Brunton SL, Noack B, Koumoutsakos P (2020) Machine learning for fluid mechanics. In: Davis S, Moin P(eds) Annual review of fluid mechanics, 52: 477–508. https://doi.org/10.1146/annurev-fluid-010719-060214

  4. Carroll TL (2018) Using reservoir computers to distinguish chaotic signals. Phys Rev E. https://doi.org/10.1103/PhysRevE.98.052209

    Article  Google Scholar 

  5. Chen C, Liu Z, Feng S (2018) Universal approximation capability of broad learning system and its structural variations. IEEE Trans Neural Netw Learn Syst 30(4):1191–1204. https://doi.org/10.1109/TNNLS.2018.2866622

    Article  MathSciNet  Google Scholar 

  6. Chen P, Liu R, Aihara K, Chen L (2020) Autoreservoir computing for multistep ahead prediction based on the spatiotemporal information transformation. Nat Commun. https://doi.org/10.1038/s41467-020-18381-0

    Article  Google Scholar 

  7. Fan H, Jiang J, Zhang C, Wang X, Lai Y (2020) Long-term prediction of chaotic systems with recurrent neural networks

  8. Kawakami K (2008) Supervised sequence labelling with recurrent neural networks. Ph. D. thesis

    Google Scholar 

  9. Haynes ND, Soriano MC, Rosin DP, Fischer I, Gauthier DJ (2015) Reservoir computing with a single time-delay autonomous Boolean node. Phys Rev E. https://doi.org/10.1103/PhysRevE.91.020801

    Article  Google Scholar 

  10. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735

    Article  Google Scholar 

  11. Jiang J, Lai YC (2019) Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius. Phys Rev Res. https://doi.org/10.1103/PhysRevResearch.1.033056

    Article  Google Scholar 

  12. Larger L, Baylon Fuentes A, Martinenghi R, Udaltsov VS, Chembo YK, Jacquot M (2017) High-speed photonic reservoir computing using a time-delay-based architecture: million words per second classification. Phys Rev X. https://doi.org/10.1103/PhysRevX.7.011015

    Article  Google Scholar 

  13. Lu Z, Pathak J, Hunt B, Girvan M, Brockett R (2017) Reservoir observers: model-free inference of unmeasured variables in chaotic systems. Chaos 10(1063/1):4979665

    Google Scholar 

  14. Pathak J, Lu Z, Hunt BR, Girvan M, Ott E (2017) Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data. Chaos 10(1063/1):5010300

    MathSciNet  MATH  Google Scholar 

  15. Pathak J, Wikner A, Fussell R, Chandra S, Hunt BR, Girvan M, Ott E (2018) Hybrid forecasting of chaotic processes: using machine learning in conjunction with a knowledge-based model. Chaos 10(1063/1):5028373

    MathSciNet  Google Scholar 

  16. Sirignano J, Spiliopoulos K (2018) Journal of computational physics. Ann Rev Fluid Mech. https://doi.org/10.1016/j.jcp.2018.08.029

    Article  Google Scholar 

  17. Takens F (1981) Detecting strange attractors in turbulence. In: David R, Sang YL (eds) Dynamical systems and turbulence. Springer, Berlin, pp 366–381

    Google Scholar 

  18. Yuan X, Li L, Wang Y (2020) Nonlinear dynamic soft sensor modeling with supervised long short-term memory network. IEEE Trans Industr Inf 16(5):3168–3176. https://doi.org/10.1109/TII.2019.2902129

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Nos. U1806203 and 61533011).

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Authors and Affiliations

  1. Institute of Marine Science and Technology, Shandong University, Qingdao, Shandong, 266237, China

    Yin Wang

  2. School of Control Science and Engineering, Shandong University, Jinan, Shandong, 250061, China

    Shutang Liu

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  1. Yin Wang
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  2. Shutang Liu
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Correspondence to Shutang Liu.

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Wang, Y., Liu, S. Short-term data-based spatial parallel autoreservoir computing on spatiotemporally chaotic system prediction. Neural Comput & Applic 34, 8713–8722 (2022). https://doi.org/10.1007/s00521-021-06854-2

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