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This study introduces a data-driven method to accurately model nonlinear dynamical systems without known equations. It enables precise characterization of system behaviors, especially under large inputs, using isostable reduction.

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Area of Science:

  • Nonlinear dynamical systems analysis
  • Data-driven modeling
  • Control theory

Background:

  • Isostable reduction characterizes nonlinear systems using Koopman operator eigenfunctions.
  • Accurate isostable models are computable when system dynamics are known.
  • Estimating isostable reduced equations from data is challenging, particularly for large inputs.

Purpose of the Study:

  • Develop a data-driven strategy for high-accuracy isostable reduced models of nonlinear systems with fixed point attractors.
  • Address limitations in current methods for inferring isostable models from data, especially under large input conditions.

Main Methods:

  • Analyzed steady-state outputs of nonlinear systems under sinusoidal forcing.
  • Estimated isostable response functions and isostable-to-output relationships from system data.
  • Utilized an expansion in isostable coordinates for arbitrary accuracy.

Main Results:

  • A purely data-driven inference strategy for high-accuracy isostable reduced models was developed.
  • The method successfully estimated isostable response functions and output relationships.
  • Demonstrated effectiveness on a synaptically coupled neuron population and the 1D Burgers' equation.

Conclusions:

  • The proposed data-driven method provides reliable estimates for isostable reduced models, even when system dynamics are unknown.
  • This approach is crucial for accurately modeling systems subjected to large magnitude inputs.
  • High-accuracy inference is essential for understanding complex nonlinear system behaviors in data-rich scenarios.