Learning Coherent Clusters in Weakly-Connected Network Systems

TL;DR

This paper introduces a spectral clustering-based model reduction technique for large-scale dynamic networks, effectively identifying coherent groups and approximating their interactions with quantifiable error bounds.

Contribution

It presents a novel structure-preserving reduction method that captures group dynamics and inter-group interactions in large networks, with theoretical error bounds.

Findings

Spectral clustering accurately identifies coherent groups.

Reduced models effectively approximate original network dynamics.

Theoretical error bounds are validated through numerical experiments.

Abstract

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the network feedback. Then, a reduced network is built, where each node represents the aggregate dynamics of each coherent group, and the reduced network captures the dynamic coupling between the groups. We provide an upper bound on the approximation error when the network graph is randomly generated from a weight stochastic block model. Finally, numerical experiments align with and validate our theoretical findings.