Inferring networks from time series: A neural approach.

Area of Science:

• Complex Systems Science
• Computational Neuroscience
• Network Science

Background:

• Complex network structures are fundamental to many systems but are often unobservable.
• Inferring network connectivity from observed dynamics is crucial for understanding these systems.

Purpose of the Study:

• To develop a computational method for inferring large network adjacency matrices from time series data.
• To provide uncertainty quantification in network inference, addressing data noise and underdetermined problems.

Main Methods:

• Utilized a neural network approach for inferring network adjacency matrices from time series data.
• Applied the method to infer line failure locations in the British power grid.
• Demonstrated extension to nonlinear dynamics by learning a cost matrix for an economic model.

Main Results:

• The method provides probability densities on network edges, enabling probabilistic statements.
• Achieved higher accuracy than Markov-chain Monte Carlo sampling and least squares regression, especially with noisy or underdetermined data.
• Successfully inferred network structures in both linear (power grid) and nonlinear (economic model) systems.

Conclusions:

• The developed neural network method offers a powerful and generalizable approach for network inference with uncertainty quantification.
• This technique advances the understanding of complex systems by accurately inferring hidden network structures.
• The method serves as a general parameter estimation scheme applicable to diverse high-dimensional problems.