Unravelled multilevel transformation networks for predicting sparsely observed spatio-temporal dynamics

In this paper, we address the problem of predicting complex, nonlinear spatio-temporal dynamics when available data are recorded at irregularly spaced sparse spatial locations. Most of the existing deep learning models for modelling spatio-temporal 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 spatio-temporal dynamics using data from sparsely-distributed data sites. We base our approach on the radial basis function (RBF) collocation method which is often used for meshfree solution of partial differential equations. The RBF framework allows us to unravel the observed spatio-temporal 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. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.