A LSTM based prediction model for nonlinear dynamical systems with chaotic itinerancy

Abstract

The prediction for chaotic trajectory from the measured data of time history, without prior knowledge of underlying dynamical model, is a challenging task in the data-driven analysis, due to its sensitivity to initial conditions. In this paper, the Long Short-Term Memory Network (LSTM) with the merge layer is proposed to predict the future states of the coupled Morris-Lecar (M-L) system with the chaotic itinerancy responses. Here, the two LSTM models with single-branch and multi-branch are constructed respectively to carry out the predictions in the multivariate loading conditions. By comparison to the network model with single-branch, the multi-branch model with adding merge layer can provide a high utilization of weights to reduce training cost greatly and receive a low prediction error, which make the multi-layer LSTM promising to estimate a high-dimensional complex dynamical behavior like transient chaotic itinerancy.

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Acknowledgement

The work is supported by the National Natural Science Foundation of China under 11772243.

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Correspondence to Jun Jiang.

Appendix A

Appendix A

The network structure diagram built after adding the merge layer

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Xue, Y., Jiang, J. & Hong, L. A LSTM based prediction model for nonlinear dynamical systems with chaotic itinerancy. Int. J. Dynam. Control (2020). https://doi.org/10.1007/s40435-020-00673-4

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Keywords

  • Nonlinear dynamical systems
  • Chaotic itinerancy
  • Time series prediction
  • Multivariate loading conditions