  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.
