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We introduce higher-order Granger reservoir computing (HoGRC), a novel framework for predicting complex dynamics. HoGRC enhances prediction accuracy and maintains model simplicity by inferring higher-order structures using Granger causality.

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Area of Science:

  • Complex Systems
  • Machine Learning
  • Dynamical Systems

Background:

  • Machine learning, particularly reservoir computing (RC), excels at predicting complex dynamics.
  • A key challenge is improving prediction accuracy without increasing model complexity.

Purpose of the Study:

  • To develop a data-driven, model-free framework, higher-order Granger reservoir computing (HoGRC).
  • To infer higher-order structures using Granger causality and enable multi-step time series prediction.

Main Methods:

  • HoGRC framework integrates Granger causality with reservoir computing.
  • It infers higher-order temporal dependencies from time series data.
  • The inferred structures are used alongside time series for multi-step prediction.

Main Results:

  • HoGRC demonstrates efficacy and robustness across diverse systems.
  • Tested on chaotic systems, network dynamics, and the UK power grid.
  • Successfully predicted complex dynamics while maintaining low model complexity.

Conclusions:

  • HoGRC offers a powerful approach for structure inference and dynamics prediction.
  • Anticipated broad applications in machine learning and complex systems research.
  • Advances the state-of-the-art in predictive modeling for dynamic systems.