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.

From earth system sciences to climate modeling and ecology, many of the greatest empirical modeling challenges are geographic in nature. As these processes are characterized by spatial dynamics, we can exploit their autoregressive nature to inform learning algorithms. We introduce SXL, a method for learning with geospatial data using explicitly spatial auxiliary tasks. We embed the local Moran's I, a well-established measure of local spatial autocorrelation, into the training process, "nudging" the model to learn the direction and magnitude of local autoregressive effects in parallel with the primary task. Further, we propose an expansion of Moran's I to multiple resolutions to capture effects at different spatial granularities and over varying distance scales. We show the superiority of this method for training deep neural networks using experiments with real-world geospatial data in both generative and predictive modeling tasks. Our approach can be used with arbitrary network architectures and, in our experiments, consistently improves their performance. We also outperform appropriate, domain-specific interpolation benchmarks. Our work highlights how integrating the geographic information sciences and spatial statistics into machine learning models can address the specific challenges of spatial data.