Data-driven inference of high-accuracy isostable-based dynamical models in response to external inputs.

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.