Geographically and temporally convolutional neural network weighted regression for modelling spatiotemporal non-stationarity on uneven data

Uneven spatial and temporal sampling is an inherent feature of geographic data. Although not intrinsically problematic, such irregularity can destabilize local estimates when observations are sparse, particularly in geographically and temporally weighted regression, where limited local support amplifies variance and undermines predictive reliability. We introduce a Geographically and Temporally Convolutional Neural Network Weighted Regression (GTCNNWR) model to improve local estimation stability without altering the original sampling configuration. The approach constructs a Global Spatial Proximity Grid (GSPG) and a Global Temporal Proximity Axis (GTPA) as fixed reference frames for feature extraction, providing consistent neighborhood representations without regularizing or resampling spatial and temporal units. Convolutional neural networks extract spatial and temporal proximity features from these reference structures, enabling each observation to integrate broader contextual information while preserving local variation. Tests on simulated datasets and real environmental data exhibiting pronounced sampling heterogeneity show that GTCNNWR enhances coefficient estimation stability and predictive performance. In sparsely sampled regions, the testing R2 increases from 0.847 to 0.874 in simulations and improves by approximately 21% in real-world applications. These results demonstrate that stabilizing local estimation in data-sparse areas can substantially improve model performance. GTCNNWR provides a practical and scalable framework for modelling spatiotemporal non-stationarity under uneven sampling.