Learning Coarse-Grained Dynamics on Graph

Yin Yu; John Harlim; Daning Huang; Yan Li

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arXiv · 2405.09324

Learning Coarse-Grained Dynamics on Graph

Yin Yu·John Harlim·Daning Huang·Yan Li

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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.

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math.NA cond-mat.dis-nn cs.LG cs.NA

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Yin Yu, John Harlim, Daning Huang, Yan Li. 2024-05-15. Learning Coarse-Grained Dynamics on Graph. https://arxiv.org/abs/2405.09324

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