As a powerful predictive technique based on machine learning, the maximum entropy (MaxEnt) model has been widely used in geographic modeling. However, its performance in calibrating cellular automata (CA) for urban growth simulation has not been investigated. This study compares the MaxEnt model with logistic regression (LR), artificial neural network (ANN), and support vector machine (SVM) models to explore its advantages in simulating urban growth and interpreting driving mechanisms. With the land use data of 2000 and 2020 from GlobeLand30, the constructed LR-CA, ANN-CA, SVM-CA, and MaxEnt-CA models are applied to simulate the urban growth of Beijing, Tianjin, and Wuhan, respectively. Their performance has been evaluated from multiple aspects such as the accuracy of training, testing, and projecting, computational efficiency, simulation accuracy, and simulated urban landscape. The results indicate that the MaxEnt model is superior to the other models except for the computational efficiency, but the time required for the MaxEnt training and projecting is acceptable and far less than that of the SVM. Taking the LR-CA as the benchmark, the kappa coefficients (Kappa) of the MaxEnt-CA have been increased by 4.20%, 3.38%, and 5.87% in Beijing, Tianjin, and Wuhan, respectively; the increments of corresponding figure of merits (FoM) are 6.26%, 4.58%, and 8.49%. The driving mechanisms of urban growth such as the interactions, response curves, and importance of spatial variables, have also been revealed by the MaxEnt modeling. The driving mechanisms of urban growth in Tianjin are more complex than that in Beijing and Wuhan, because there are more variable interactions; the relationships between spatial factors and urban growth in the three study areas are all nonlinear; the topographic factors and city center of Beijing, the traffic factors and water bodies of Tianjin, and the traffic factors, city center and water bodies of Wuhan are significant factors affecting their urban growth.

The stochastic perturbation of urban cellular automata (CA) model is difficult to fine-tune and does not take the constraint of known factors into account when using a stochastic variable, and the simulation results can be quite different when using the Monte Carlo method, reducing the accuracy of the simulated results. Therefore, in this paper, we optimize the stochastic component of an urban CA model by the use of a maximum entropy model to differentially control the intensity of the stochastic perturbation in the spatial domain. We use the kappa coefficient, figure of merit, and landscape metrics to evaluate the accuracy of the simulated results. Through the experimental results obtained for Wuhan, China, the effectiveness of the optimization is proved. The results show that, after the optimization, the kappa coefficient and figure of merit of the simulated results are significantly improved when using the stochastic variable, slightly improved when using Monte Carlo methods. The landscape metrics for the simulated results and actual data are much closer when using the stochastic variable, and slightly closer when using the Monte Carlo method, but the difference between the simulated results is narrowed, reflecting the fact that the results are more reliable.

Although the neighborhood of the cellular automata (CA) model has been studied in detail, there is a contradiction in the selection of the neighborhood size that has not been revealed and addressed. The contradiction is that small neighborhoods can constrain the shape complexity of the simulated landscape, but they cannot sufficiently characterize the local interactions, while large neighborhoods do the opposite. In this paper, we propose a new type of dual-scale neighborhood (DSN) based on vectorization to avoid this contradiction. Taking Beijing, Wuhan, and the Pearl River Delta in China as study areas, two kinds of CA models, namely, the CA model using the original neighborhood (ORN-CA) and the CA model using the proposed DSN (DSN-CA), were constructed based on the serial/scalar algorithm and the vectorized algorithm, respectively. The comparison of the simulation results and the time taken shows that the DSN enables the user to choose the appropriate neighborhood configuration to obtain high-accuracy simulation results and a landscape that is similar to the ground truth. The vectorization can also greatly improve the computational efficiency of the neighborhood effects. Overall, the findings show that integrating the DSN with vectorization can significantly improve the simulation performance and efficiency of CA models.