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Deterministic reservoir computing for chaotic time series prediction.

Johannes Viehweg1, Constanze Poll2, Patrick Mäder2,3

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This study introduces deterministic Reservoir Computing models, TCRC-LM and TCRC-CM, using Logistic and Chebyshev maps. These novel networks enhance time series forecasting accuracy, outperforming existing methods like Echo State Networks.

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Computational Neuroscience

Background:

  • Reservoir Computing (RC) offers efficient learning for time series tasks.
  • Randomized initialization in RC aids computation but hinders theoretical analysis.
  • Deterministic RC variations are crucial for advancing the field.

Purpose of the Study:

  • To develop deterministic alternatives to higher-dimensional mappings in Reservoir Computing.
  • To enhance time series forecasting performance using novel deterministic networks.
  • To investigate the efficacy of the Lobachevsky function as a non-linear activation.

Main Methods:

  • Proposed TCRC-LM and TCRC-CM models utilizing Logistic and Chebyshev maps.
  • Implemented the Lobachevsky function as a non-linear activation function.
  • Evaluated performance against Echo State Networks and Temporal Convolution Derived Reservoir Computing (TCRC).

Main Results:

  • The novel deterministic networks, TCRC-LM and TCRC-CM, demonstrated superior performance.
  • Outperformed classical Reservoir Computing (Echo State Networks) by up to on non-chaotic and on chaotic time series.
  • Achieved enhanced predictive capabilities in time series forecasting tasks.

Conclusions:

  • A fully deterministic Reservoir Computing network was successfully developed.
  • The proposed models offer significant improvements in time series forecasting accuracy.
  • This research opens new avenues for deterministic Reservoir Computing applications.