This paper proposes a temporal graph neural network model for forecasting of graph-structured irregularly observed time series. Our TGNN4I model is designed to handle both irregular time steps and partial observations of the graph. This is achieved by introducing a time-continuous latent state in each node, following a linear Ordinary Differential Equation (ODE) defined by the output of a Gated Recurrent Unit (GRU). The ODE has an explicit solution as a combination of exponential decay and periodic dynamics. Observations in the graph neighborhood are taken into account by integrating graph neural network layers in both the GRU state update and predictive model. The time-continuous dynamics additionally enable the model to make predictions at arbitrary time steps. We propose a loss function that leverages this and allows for training the model for forecasting over different time horizons. Experiments on simulated data and real-world data from traffic and climate modeling validate the usefulness of both the graph structure and time-continuous dynamics in settings with irregular observations.

翻译：本文提出了一种面向图结构不规则观测时间序列预测的时序图神经网络模型。所提出的TGNN4I模型可同时处理不规则时间步长与图的部分观测问题。通过在每个节点引入遵循门控循环单元（GRU）输出定义的线性常微分方程（ODE）的时间连续隐状态，该模型得以实现。该常微分方程具有由指数衰减与周期动力学组合构成的显式解。通过在GRU状态更新与预测模型中集成图神经网络层，可有效利用图邻域内的观测信息。时间连续动力学特性使模型能够对任意时间步长进行预测。我们提出了一种利用该特性的损失函数，可训练模型对不同预测时间跨度进行预测。在模拟数据及交通与气候建模领域真实数据上的实验验证了：在存在不规则观测的场景中，图结构与时间连续动力学特性均具有实用价值。