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Discovering network dynamics with neural symbolic regression.

Zihan Yu1, Jingtao Ding2, Yong Li3

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Summary

This study introduces a neural symbolic regression method to automatically discover mathematical models for complex network dynamics from data. This approach enhances understanding of systems and advances complexity science.

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Area of Science:

  • Complexity Science
  • Network Science
  • Machine Learning

Background:

  • Analyzing high-dimensional complex systems requires understanding their network dynamics.
  • Mathematical models for these systems are scarce, limiting analysis despite abundant data.
  • Existing models often lack clear underlying principles.

Purpose of the Study:

  • To develop a method for automatically deriving mathematical formulas for network dynamics from observational data.
  • To bridge the gap between data availability and model development in complex systems.
  • To enhance the understanding and prediction capabilities of complex systems.

Main Methods:

  • Utilized a neural symbolic regression approach to automatically derive formulas from data.
  • Reduced high-dimensional network searches to equivalent one-dimensional systems.
  • Employed pretrained neural networks to guide accurate formula discovery.

Main Results:

  • Successfully recovered correct forms and parameters for ten benchmark systems.
  • Improved prediction accuracy in gene regulation (59.98%) and microbial communities (55.94%).
  • Discovered epidemic transmission dynamics on human mobility networks, revealing scale-invariant properties and country-level intervention effects.

Conclusions:

  • Machine-driven discovery of network dynamics significantly enhances the understanding of complex systems.
  • This approach advances the field of complexity science by enabling model creation from data.
  • The method shows broad applicability across theoretical and empirical systems.