Geographically and temporally neural network weighted regression for modeling spatiotemporal non-stationary relationships

Geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR) are classic methods for estimating non-stationary relationships. Although these methods have been widely used in geographical modeling and spatiotemporal analysis, they face challenges in adequately expressing space-time proximity and constructing a kernel with optimal weights. This probably results in an insufficient estimation of spatiotemporal non-stationarity. To address complex non-linear interactions between time and space, a spatiotemporal proximity neural network (STPNN) is proposed in this paper to accurately generate space-time distance. A geographically and temporally neural network weighted regression (GTNNWR) model that extends geographically neural network weighted regression (GNNWR) with the proposed STPNN is then developed to effectively model spatiotemporal non-stationary relationships. To examine its performance, we conducted two case studies of simulated datasets and environmental modeling in coastal areas of Zhejiang, China. The GTNNWR model was fully evaluated by comparing with ordinary linear regression (OLR), GWR, GNNWR, and GTWR models. The results demonstrated that GTNNWR not only achieved the best fitting and prediction performance but also exactly quantified spatiotemporal non-stationary relationships. Further, GTNNWR has the potential to handle complex spatiotemporal non-stationarity in various geographical processes and environmental phenomena.