Learning Coherent Clusters in Weakly-Connected Network Systems
This work addresses model reduction for large-scale network systems, but it appears incremental as it builds on existing spectral clustering and stochastic block model techniques.
The authors tackled the problem of model reduction for large-scale dynamic networks with tightly-connected components by identifying coherent groups via spectral clustering and constructing a reduced network that captures inter-group dynamics, providing an upper bound on approximation error for randomly generated networks and validating results with numerical experiments.
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.