  Graph-based spatio-temporal neural networks are effective to model the
spatial dependency among discrete points sampled irregularly from unstructured
grids, thanks to the great expressiveness of graph neural networks. However,
these models are usually spatially-transductive -- only fitting the signals for
discrete spatial nodes fed in models but unable to generalize to `unseen'
spatial points with zero-shot. In comparison, for forecasting tasks on
continuous space such as temperature prediction on the earth's surface, the
\textit{spatially-inductive} property allows the model to generalize to any
point in the spatial domain, demonstrating models' ability to learn the
underlying mechanisms or physics laws of the systems, rather than simply fit
the signals. Besides, in temporal domains, \textit{irregularly-sampled} time
series, e.g. data with missing values, urge models to be temporally-continuous.
Motivated by the two issues, we propose a spatio-temporal framework based on
neural operators for PDEs, which learn the underlying mechanisms governing the
dynamics of spatially-continuous physical quantities. Experiments show our
model's improved performance on forecasting spatially-continuous physic
quantities, and its superior generalization to unseen spatial points and
ability to handle temporally-irregular data.
