  Explosive growth in spatio-temporal data and its wide range of applications
have attracted increasing interests of researchers in the statistical and
machine learning fields. The spatio-temporal regression problem is of paramount
importance from both the methodology development and real-world application
perspectives. Given the observed spatially encoded time series covariates and
real-valued response data samples, the goal of spatio-temporal regression is to
leverage the temporal and spatial dependencies to build a mapping from
covariates to response with minimized prediction error. Prior arts, including
the convolutional Long Short-Term Memory (CovLSTM) and variations of the
functional linear models, cannot learn the spatio-temporal information in a
simple and efficient format for proper model building. In this work, we propose
two novel extensions of the Functional Neural Network (FNN), a temporal
regression model whose effectiveness and superior performance over alternative
sequential models have been proven by many researchers. The effectiveness of
the proposed spatio-temporal FNNs in handling varying spatial correlations is
demonstrated in comprehensive simulation studies. The proposed models are then
deployed to solve a practical and challenging precipitation prediction problem
in the meteorology field.
