Inference of the size of nonlinear network systems from perceptible dynamics

Area of Science:

• Network science
• Dynamical systems theory
• Systems engineering

Background:

• Network dynamical systems are fundamental across various scientific and engineering disciplines.
• Determining the size (number of nodes) of linear network systems from partial measurements is established.
• Extending size inference to nonlinear network systems remains a significant challenge.

Purpose of the Study:

• To develop a model-agnostic method for inferring the size of nonlinear network dynamical systems.
• To provide tools for analyzing complex systems where governing equations are unknown.
• To enable size estimation from limited, observable dynamics.

Main Methods:

• A novel approach combining clustering techniques, detection matrices, and spectral analysis.
• Utilizing variations in perceptible node dynamics across multiple measurements to bound system dynamics.
• Applying clustering to identify regions where dynamics are approximately linear for valid detection matrix application.

Main Results:

• Successfully inferred the size of nonlinear network systems, including hypergraphs, using the proposed method.
• Demonstrated the effectiveness of the approach through numerical experiments.
• The rank of the detection matrix spectrum directly corresponds to the nonlinear network system's size.

Conclusions:

• The developed method provides a robust way to infer the size of nonlinear network systems from limited data.
• This approach is applicable even when the underlying equations governing the system are unknown.
• The findings pave the way for analyzing complex nonlinear networks in various scientific domains.