@article{yu2025,
	title = {Learning coarse-grained dynamics on graph},
	volume = {481},
	issn = {0167-2789},
	doi = {10.1016/j.physd.2025.134801},
	abstract = {We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the Mori-Zwanzig memory term depends on the coarse-grained interaction coefficients that encode the graph topology. Based on this analysis, we found that the appropriate GNN architecture that will account for K-hop dynamical interactions has to employ a Message Passing (MP) mechanism with at least 2K steps. We also deduce that the memory length required for an accurate closure model decreases as a function of the interaction strength under the assumption that the interaction strength exhibits a power law that decays as a function of the hop distance. Supporting numerical demonstrations on two examples, a heterogeneous Kuramoto oscillator model and a power system, suggest that the proposed GNN architecture can predict the coarse-grained dynamics under fixed and time-varying graph topologies.},
	urldate = {2026-03-20},
	journal = {Physica D: Nonlinear Phenomena},
	author = {Yu, Yin and Harlim, John and Huang, Daning and Li, Yan},
	month = nov,
	year = {2025},
	note = {yu2025},
	keywords = {Coarse-graining, Graph neural network, Networked dynamics, Non-markovian modeling, Time-varying topology},
	pages = {134801},
}

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