A hybrid modeling approach considering spatial heterogeneity and nonlinearity to discover the transition rules of urban cellular automata models

Urban sprawl is a typical geographic dynamic process with spatial heterogeneity and nonlinearity. However, current studies usually focus on only one of them to extract urban sprawl mechanisms and build cellular automata (CA) models. In the current work, the urban CA transition rules are derived by a geographically weighted artificial neural network (GWANN), which can discover the driving mechanism of urban sprawl by considering both spatial heterogeneity and nonlinearity. Taking the urban sprawl of Wuhan and Beijing during 2000–2020 as examples, the advantages of GWANN in deriving transition rules are investigated by comparing it with logistic regression (LR), geographically weighted logistic regression (GWLR), and artificial neural network (ANN). Furthermore, the simulation performance of CA models based on LR, GWLR, ANN, and GWANN is compared and analyzed from the aspects of global and regional simulation accuracy and the morphology of simulated urban patches. The results show that GWANN has better fitting and simulation performance, indicating the validity and necessity of coupling spatial heterogeneity and nonlinearity to establish transition rules. This study is a novel exploration that contributes to deriving CA transition rules through a hybrid modeling approach that couples statistical models with learning models.