STONet: A Neural-Operator-Driven Spatio-temporal Network

Abstract: 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.