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Predicting nonsmooth chaotic dynamics by reservoir computing.

Lufa Shi1, Hengtong Wang1, Shengjun Wang1

  • 1School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China.

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Reservoir computing (RC) can now predict nonsmooth dynamics using a new piecewise activation function. This physics-informed approach enables accurate short- and long-term predictions for complex systems.

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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Computational Science and Engineering

Background:

  • Reservoir computing (RC) is effective for predicting chaotic dynamics.
  • Nonsmooth dynamics, crucial in many fields, remain largely unexplored by RC.

Purpose of the Study:

  • Generalize reservoir computing to effectively model nonsmooth dynamical systems.
  • Introduce a novel activation function tailored for nonsmooth dynamics.

Main Methods:

  • Developed a physics-informed RC scheme utilizing a piecewise nonsmooth activation function.
  • Tested the scheme on four distinct nonsmooth systems: tent map, piecewise linear map with gap, compound circle maps, and Lozi map.

Main Results:

  • Conventional RC with hyperbolic tangent activation struggles with nonsmooth systems, especially long-term prediction.
  • The proposed RC scheme with a nonsmooth activation function accurately predicts both short- and long-term dynamics.
  • Prediction precision for attractor reconstruction correlates with system complexity.

Conclusions:

  • The activation function's nature (smooth vs. nonsmooth) must align with the dynamical system for efficient RC predictions.
  • This work extends RC capabilities to a broader class of important dynamical systems.