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Infinite-dimensional next-generation reservoir computing.

Lyudmila Grigoryeva1, Hannah Lim Jing Ting2, Juan-Pablo Ortega2

  • 1Universität Sankt Gallen, Mathematics and Statistics Division, CH-9000, Switzerland.

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Summary
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Next-generation reservoir computing (NG-RC) is now more efficient and adaptable. This advanced method, framed as kernel ridge regression, improves spatiotemporal forecasting for complex systems.

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Area of Science:

  • Complex Systems Science
  • Machine Learning
  • Computational Neuroscience

Background:

  • Next-generation reservoir computing (NG-RC) shows promise for complex system spatiotemporal forecasting.
  • Traditional NG-RC faces challenges with large feature spaces and hyperparameter tuning.

Purpose of the Study:

  • To demonstrate that NG-RC can be efficiently implemented using kernel ridge regression.
  • To introduce an extended NG-RC methodology with infinite covariates, enhancing adaptability.
  • To provide theoretical backing and empirical validation for the proposed approach.

Main Methods:

  • Encoding NG-RC as kernel ridge regression for computational efficiency.
  • Developing an extension to infinite covariates, removing limitations on past lags and polynomial features.
  • Leveraging kernel universality properties for theoretical analysis.

Main Results:

  • The kernel ridge regression formulation makes NG-RC training efficient and feasible for large feature spaces.
  • The extended methodology is agnostic to the number of past lags and polynomial covariates.
  • Numerical results demonstrate superior forecasting performance compared to traditional NG-RC.

Conclusions:

  • The proposed kernel-based NG-RC offers a theoretically sound and practically superior alternative for spatiotemporal forecasting.
  • This generalization enhances the applicability and performance of reservoir computing for complex systems.