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Summary
This summary is machine-generated.

More data can degrade deep neural network performance. In this study, we found that excessive data can cause instability in data-driven dynamical system models, specifically next-generation reservoir computing (NGRC).

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Area of Science:

  • Dynamical Systems
  • Machine Learning
  • Computational Neuroscience

Background:

  • Deep neural networks can experience performance degradation with excessive data.
  • Data-driven models are increasingly used for understanding complex dynamical systems.

Purpose of the Study:

  • To investigate the phenomenon of data-induced instability in next-generation reservoir computing (NGRC).
  • To elucidate the mechanisms behind performance degradation in NGRC with increasing data.
  • To propose strategies for mitigating data-induced instability in NGRC.

Main Methods:

  • Focusing on next-generation reservoir computing (NGRC) as a framework for learning dynamics.
  • Analyzing the impact of increased training data on the model's representation of the flow map.
  • Investigating the role of auxiliary dimensions from delayed states in NGRC stability.
  • Proposing regularization and noise injection as mitigation strategies.

Main Results:

  • Increased training data, while improving flow map representation, can lead to ill-conditioned integrators and instability in NGRC.
  • Data-induced instability is linked to auxiliary dimensions created by delayed states in NGRC.
  • Strategies like increased regularization and careful noise injection can mitigate this instability.

Conclusions:

  • Proper regularization is crucial for stable and reliable data-driven modeling of dynamical systems.
  • Understanding the trade-offs between data size and model stability is essential for NGRC applications.
  • The findings offer practical approaches to enhance the robustness of NGRC models.