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Deep geometric neural network for spatial interpolation

Spatial interpolation is the task to interpolate the targeted index, such as PM2.5 values and temperature, at arbitrary locations based on the collected geospatial data. It greatly affects the key research topics in geoscience in terms of obtaining heterogeneous spatial information (e.g., soil conditions, precipitation rates, wheat yields) for geographic modeling and decision-making at local, regional, and global scales. Point-based data, collected by ground-level in-situ sensors, serve as an important data source for this task. However, several major challenges still exist: point-based data are sparse and unevenly distributed. More importantly, it is difficult to model the unknown spatial predictive mapping while handling the trade-off between spatial autocorrelation and heterogeneity. Third, representing spatial relations without substantial information loss is also a critical issue. To address these challenges, we propose a novel Deep Geometric Spatial Interpolation (DGSI) framework as the interpolation backbone that automatically interpolates the targeted index at unknown locations based on existing observations. Our proposed model takes into account both distance and orientation information, which is proven to preserve spatial information. Extensive experiments have been conducted on real-world datasets and demonstrated our model's superiority in performance over state-of-the-art models.