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Learning coarse-grained dynamics on graph
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DOI：10.1016/j.physd.2025.134801.png)
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Abstract
En 中文
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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P
IF:
2.9
Papers:
389
Citations:
1.5W
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