Coarse-graining network flow through statistical physics and machine learning.

Area of Science:

• Complex systems science
• Statistical physics
• Network science

Background:

• Information dynamics is vital in complex systems, with statistical physics offering tools like entropy and free energy to analyze network properties.
• Analyzing large-scale networks is computationally challenging, limiting practical applications of information dynamics.
• Existing methods often focus on network structure, potentially overlooking functional information flow.

Purpose of the Study:

• To develop a computationally efficient method for compressing large complex networks.
• To preserve critical information flow dynamics during network compression.
• To enable multiscale analysis of complex systems.

Main Methods:

• Utilized graph neural networks (GNNs) to identify components suitable for network coarse-graining.
• Developed a GNN-based approach for low-complexity network compression.
• Validated the method through theoretical analysis and experiments on synthetic and empirical networks.

Main Results:

• The GNN approach achieved significant network compression with low computational complexity.
• Information flow, including flow diversity and signal speed, was preserved under substantial compression.
• The model merged nodes with similar structural properties, indicating redundant roles in information transmission.
• The method demonstrated superior preservation of information flow compared to structure-focused methods.

Conclusions:

• Graph neural networks offer an effective solution for compressing extremely large networks while preserving information flow.
• This multiscale perspective enhances the analysis of information dynamics in biological, social, and technological systems.
• The approach provides a computationally feasible way to study complex systems at different scales.