  In this paper, we address the problem of predicting complex, nonlinear
spatiotemporal dynamics when available data is recorded at irregularly-spaced
sparse spatial locations. Most of the existing deep learning models for
modeling spatiotemporal dynamics are either designed for data in a regular grid
or struggle to uncover the spatial relations from sparse and irregularly-spaced
data sites. We propose a deep learning model that learns to predict unknown
spatiotemporal dynamics using data from sparsely-distributed data sites. We
base our approach on Radial Basis Function (RBF) collocation method which is
often used for meshfree solution of partial differential equations (PDEs). The
RBF framework allows us to unravel the observed spatiotemporal function and
learn the spatial interactions among data sites on the RBF-space. The learned
spatial features are then used to compose multilevel transformations of the raw
observations and predict its evolution in future time steps. We demonstrate the
advantage of our approach using both synthetic and real-world climate data.
