  Graph neural networks (GNNs) provide a powerful and scalable solution for
modeling continuous spatial data. However, they often rely on Euclidean
distances to construct the input graphs. This assumption can be improbable in
many real-world settings, where the spatial structure is more complex and
explicitly non-Euclidean (e.g., road networks). Here, we propose PE-GNN, a new
framework that incorporates spatial context and correlation explicitly into the
models. Building on recent advances in geospatial auxiliary task learning and
semantic spatial embeddings, our proposed method (1) learns a context-aware
vector encoding of the geographic coordinates and (2) predicts spatial
autocorrelation in the data in parallel with the main task. On spatial
interpolation and regression tasks, we show the effectiveness of our approach,
improving performance over different state-of-the-art GNN approaches. We
observe that our approach not only vastly improves over the GNN baselines, but
can match Gaussian processes, the most commonly utilized method for spatial
interpolation problems.
