Learning Coherent Clusters in Weakly-Connected Network Systems

Hancheng Min, Enrique Mallada
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:1167-1179, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-min23a, title = {Learning Coherent Clusters in Weakly-Connected Network Systems}, author = {Min, Hancheng and Mallada, Enrique}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {1167--1179}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/min23a/min23a.pdf}, url = {https://proceedings.mlr.press/v211/min23a.html}, 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.} }
Endnote
%0 Conference Paper %T Learning Coherent Clusters in Weakly-Connected Network Systems %A Hancheng Min %A Enrique Mallada %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-min23a %I PMLR %P 1167--1179 %U https://proceedings.mlr.press/v211/min23a.html %V 211 %X 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.
APA
Min, H. & Mallada, E.. (2023). Learning Coherent Clusters in Weakly-Connected Network Systems. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:1167-1179 Available from https://proceedings.mlr.press/v211/min23a.html.

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