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.

Simulating urban landscape dynamics in metropolitan areas has attracted much attention lately, but the difficulty remains. Although large-scale urban simulation studies consider spatial interaction as an important factor, spatial interaction cannot be accurately measured based on a single element flow, and its effects may not strictly follow a distance decay function. Furthermore, different cities may require different transition rules. In this study, we combined bidirectional flows of population and information and an improved gravitational field model to model the urban spatial interaction, and we then integrated a partitioned cellular automata (CA) model to simulate the urban growth for different cities in the Yangtze River middle reaches megalopolis. It was found that the simulation results generated by the CA model considering spatial interaction are significantly improved. Furthermore, partitioned conversion thresholds can effectively improve the model performance. The proposed model showed a much better performance in the simulation of subordinate cities surrounding the core cities, than for the core cities and fringe cities. We suggest that large-scale urban simulation should pay more attention to the development of partitioned transition rules. The effects of intercity urban flows should also be considered in the simulation of small- and medium-sized cities near the regional cores.

Cellular automata (CA) models can simulate complex urban systems through simple rules and have become important tools for studying the spatio-temporal evolution of urban land use. However, the multiple and large-volume data layers, massive geospatial processing and complicated algorithms for automatic calibration in the urban CA models require a high level of computational capability. Unfortunately, the limited performance of sequential computation on a single computing unit (i.e. a central processing unit (CPU) or a graphics processing unit (GPU)) and the high cost of parallel design and programming make it difficult to establish a high-performance urban CA model. As a result of its powerful computational ability and scalability, the vectorization paradigm is becoming increasingly important and has received wide attention with regard to this kind of computational problem. This paper presents a high-performance CA model using vectorization and parallel computing technology for the computation-intensive and data-intensive geospatial processing in urban simulation. To transfer the original algorithm to a vectorized algorithm, we define the neighborhood set of the cell space and improve the operation paradigm of neighborhood computation, transition probability calculation, and cell state transition. The experiments undertaken in this study demonstrate that the vectorized algorithm can greatly reduce the computation time, especially in the environment of a vector programming language, and it is possible to parallelize the algorithm as the data volume increases. The execution time for the simulation of 5-m resolution and 3 × 3 neighborhood decreased from 38,220.43 s to 803.36 s with the vectorized algorithm and was further shortened to 476.54 s by dividing the domain into four computing units. The experiments also indicated that the computational efficiency of the vectorized algorithm is closely related to the neighborhood size and configuration, as well as the shape of the research domain. We can conclude that the combination of vectorization and parallel computing technology can provide scalable solutions to significantly improve the applicability of urban CA.

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.