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Reconstructing latent dynamical noise for better forecasting observables.

Yoshito Hirata1

  • 1Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.

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Summary
This summary is machine-generated.

This study reconstructs multi-dimensional dynamical noise to improve time series forecasting. The novel method uses past noise as auxiliary information for more accurate predictions in complex systems.

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Area of Science:

  • Dynamical systems theory
  • Nonlinear science
  • Time series analysis

Background:

  • Dynamical noise significantly impacts the predictability of complex systems.
  • Existing methods for noise reconstruction often struggle with multi-dimensional systems.
  • Accurate noise characterization is crucial for reliable forecasting.

Purpose of the Study:

  • To develop a novel method for reconstructing multi-dimensional dynamical noise.
  • To enhance time series forecasting by incorporating reconstructed noise as auxiliary information.
  • To validate the proposed method on various noise models.

Main Methods:

  • Utilizing the embedding theorem of Muldoon et al. to treat multiple predictions as observables.
  • Applying the embedding theorem by Stark et al. for forced systems.
  • Reconstructing past dynamical noise and using it for time series prediction.

Main Results:

  • Successfully reconstructed multi-dimensional dynamical noise from system predictions.
  • Demonstrated improved time series forecast accuracy by including reconstructed noise.
  • Validated the method on toy models driven by auto-regressive and Gaussian noise.

Conclusions:

  • The proposed method offers a robust approach for dynamical noise reconstruction in multi-dimensional systems.
  • Incorporating reconstructed noise as auxiliary information significantly enhances forecasting capabilities.
  • This technique holds promise for improving predictions in various fields dealing with complex dynamical systems.