Modeling spatial heterogeneity in the data generation process is essential for understanding and predicting geographical phenomena. Despite their prevalence in geospatial tasks, neural network models usually assume spatial stationarity, which could limit their performance in the presence of spatial process heterogeneity. By allowing model parameters to vary over space, several approaches have been proposed to incorporate spatial heterogeneity into neural networks. However, current geographically weighting approaches are ineffective on graph neural networks, yielding no significant improvement in prediction accuracy. We assume the crux lies in the over-fitting risk brought by a large number of local parameters. Accordingly, we propose to model spatial process heterogeneity at the regional level rather than at the individual level, which largely reduces the number of spatially varying parameters. We further develop a heuristic optimization procedure to learn the region partition adaptively in the process of model training. Our proposed spatial-heterogeneity-aware graph convolutional network, named RegionGCN, is applied to the spatial prediction of county-level vote share in the 2016 US presidential election based on socioeconomic attributes. Results show that RegionGCN achieves significant improvement over the basic and geographically weighted GCNs. We also offer an exploratory analysis tool for the spatial variation of non-linear relationships through ensemble learning of regional partitions from RegionGCN. Our work contributes to the practice of Geospatial Artificial Intelligence (GeoAI) in tackling spatial heterogeneity.

The outburst of COVID-19 in late 2019 was the start of a health crisis that shook the world and took millions of lives in the ensuing years. Many governments and health officials failed to arrest the rapid circulation of infection in their communities. The long incubation period and the large proportion of asymptomatic cases made COVID-19 particularly elusive to track. However, wastewater monitoring soon became a promising data source in addition to conventional indicators such as confirmed daily cases, hospitalizations, and deaths. Despite the consensus on the effectiveness of wastewater viral load data, there is a lack of methodological approaches that leverage viral load to improve COVID-19 forecasting. This paper proposes using deep learning to automatically discover the relationship between daily confirmed cases and viral load data. We trained one Deep Temporal Convolutional Networks (DeepTCN) and one Temporal Fusion Transformer (TFT) model to build a global forecasting model. We supplement the daily confirmed cases with viral loads and other socio-economic factors as covariates to the models. Our results suggest that TFT outperforms DeepTCN and learns a better association between viral load and daily cases. We demonstrated that equipping the models with the viral load improves their forecasting performance significantly. Moreover, viral load is shown to be the second most predictive input, following the containment and health index. Our results reveal the feasibility of training a location-agnostic deep-learning model to capture the dynamics of infection diffusion when wastewater viral load data is provided.