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Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamics

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.