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This study compares nonlinear observability with continuity statistics and reservoir computing to assess how well different signals can reconstruct dynamical systems. Results show these methods offer complementary insights into system reconstruction capabilities.

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Area of Science:

  • Dynamical Systems Analysis
  • Nonlinear Dynamics
  • Data Science

Background:

  • Reconstructing dynamical system trajectories from measured variables is crucial for analysis.
  • Nonlinear observability is a theoretical concept to determine if a system can be reconstructed from signals.
  • Calculating nonlinear observability for high-dimensional systems is computationally challenging.

Purpose of the Study:

  • To compare the effectiveness of nonlinear observability with alternative methods for assessing dynamical system reconstruction.
  • To evaluate the utility of a continuity statistic in predicting reconstructability from different signals.
  • To assess the predictive power of reservoir computing fitting errors for system reconstruction.

Main Methods:

  • Calculated nonlinear observability for dynamical systems.
  • Applied a continuity statistic to compare different trajectory reconstructions from simultaneously measured signals.
  • Utilized reservoir computing and its fitting error as a metric for signal-based system reconstruction.

Main Results:

  • Nonlinear observability predictions were compared against continuity statistics.
  • The fitting error from reservoir computer training was used as an additional validation metric.
  • The study highlights the ambiguity in predictions when lacking a clear metric for reconstruction ability.

Conclusions:

  • Nonlinear observability, continuity statistics, and reservoir computing offer complementary approaches to assess signal suitability for dynamical system reconstruction.
  • Combining these methods provides a more robust evaluation of a system's reconstructability.
  • Further research is needed to establish clear metrics for validating these reconstruction assessment techniques.