图神经常微分方程综述

  本文根据静态图、离散动态图和连续动态图等 不同类型图的特点，将相关工作分为静态图神经 ODE、 离散动态图神经 ODE 以及连续动态图神经 ODE. 根 据 ODE 所发挥的不同作用，将连续动态图神经 ODE 分为作为编码器和作为推断器 2 类 . 根据图神 经 ODE 的阶数将静态图神经 ODE 分为一阶静态图神 经 ODE 和二阶静态图神经 ODE. 此外，根据适用的 场景不同，将离散动态图神经 ODE 分为时空图神经 ODE 和多智能体神经 ODE. 本文提出的图神经 ODE 方法分类体系如下图所示.

静态图神经ODE

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离散动态图神经ODE

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连续动态图神经ODE

连续动态图ODE作为编码器

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连续动态图ODE作为推断器

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23. Liu Y, Cheng J, Zhao H, et al. Physics-Inspired Neural Graph ODE for Long-term Dynamical Simulation[J]. arXiv preprint arXiv:2308.13212, 2023.论文

连续动态图ODE作为编码器和推断器同时应用

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