Spatial interpolation is a traditional geostatistical operation that aims at predicting the attribute values of unobserved locations given a sample of data defined on point supports. However, the continuity and heterogeneity underlying spatial data are too complex to be approximated by classic statistical models. Deep learning models, especially the idea of conditional generative adversarial networks (CGANs), provide us with a perspective for formalizing spatial interpolation as a conditional generative task. In this article, we design a novel deep learning architecture named conditional encoder-decoder generative adversarial neural networks (CEDGANs) for spatial interpolation, therein combining the encoder-decoder structure with adversarial learning to capture deep representations of sampled spatial data and their interactions with local structural patterns. A case study on elevations in China demonstrates the ability of our model to achieve outstanding interpolation results compared to benchmark methods. Further experiments uncover the learned spatial knowledge in the model’s hidden layers and test the potential to generalize our adversarial interpolation idea across domains. This work is an endeavor to investigate deep spatial knowledge using artificial intelligence. The proposed model can benefit practical scenarios and enlighten future research in various geographical applications related to spatial prediction.

Inferring the unknown properties of a place relies on both its observed attributes and the characteristics of the places to which it is connected. Because place characteristics are unstructured and the metrics for place connections can be diverse, it is challenging to incorporate them in a spatial prediction task where the results could be affected by how the neighborhoods are delineated and where the true relevance among places is hard to identify. To bridge the gap, we introduce graph convolutional neural networks (GCNNs) to model places as a graph, where each place is formalized as a node, place characteristics are encoded as node features, and place connections are represented as the edges. GCNNs capture the knowledge of the relevant geographic context by optimizing the weights among graph neural network layers. A case study was designed in the Beijing metropolitan area to predict the unobserved place characteristics based on the observed properties and specific place connections. A series of comparative experiments was conducted to highlight the influence of different place connection measures on the prediction accuracy and to evaluate the predictability across different characteristic dimensions. This research enlightens the promising future of GCNNs in formalizing places for geographic knowledge representation and reasoning.

Due to the limitation of data collection techniques and privacy issues, the problem of missing spatial origin-destination flows frequently occurs. Data imputation provides great support for the acquisition of complete flow data, which enables us to better understand regional connections and mobility patterns. However, existing models or approaches neglect the network structure of spatial flows, thus resulting in inappropriate estimates and a low performance. The development of graph neural networks offers a powerful tool to deal with graph-structured data. In this article, we proposed a spatial interaction graph convolutional network model, which combines graph convolution and a mapping function to predict flow data from the perspective of network learning. This model utilizes geographical unit embedding in local spatial networks to improve prediction accuracy. A negative sampling technique is adopted to reduce misestimation. Experiments on Beijing taxi trip data verified the usefulness of our model in spatial flow prediction. We also demonstrated that a biased training sample had a negative impact on the model’s performance. More attributes of geographical units, a more proper negative sampling rate and a larger training set can increase the prediction accuracy of flow data.