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The study of multi-dimensional expansion of urban space (MEUS) addresses the laws of urban spatial expansion from all directions and angles. Using Nanjing as an example, this paper constructs multi-temporal, urban three-dimensional models based on RS and GIS technology and then conducts qualitative and quantitative analysis of MEUS using plot ratio change maps and MEUS quantitative index for built-up areas. Based especially on the concept of volume growth contribution rate, this paper analyzes the characteristics of MEUS in different stages. The results show that in 2000–2004, planar expansion played the main role, the internal potential development (IPD) intensity of the urban built-up areas was relatively large, and the volume growth contribution rate was low; in 2004–2008, planar expansion accelerated, and IPD slowed down; in 2008–2012, planar expansion slowed while IPD intensity increased; the contribution rates of volume growth of urban IPD for the three periods were 22.21%, 24.51% and 73.38%, respectively. This study expands the research perspective of urban spatial expansion, and the adopted methods are instructive and meaningful for MEUS research. In addition, the results of this study will deepen the understanding of MEUS laws and help improve scientific decision-making for urban planning and urban land use management.

In this paper, the artificial neural network (ANN) model was used to evaluate the degree of intensive urban land use in Nanjing City, China. The construction and application of the ANN model took into account the comprehensive, spatial and complex nature of urban land use. Through a preliminary calculation of the degree of intensive land use of the sample area, representative sample area selection and using the back propagation neural network model to train, the intensive land use level of each evaluation unit is finally determined in the study area. Results show that the method can effectively correct the errors caused by the limitations of the model itself and the determination of the ideal value and weights when the multifactor comprehensive evaluation is used alone. The ANN model can make the evaluation results more objective and practical. The evaluation results show a tendency of decreasing land use intensity from the core urban area to the periphery and the industrial functional area has relatively low land use intensity compared with other functional areas. Based on the evaluation results, some suggestions are put forward, such as transforming the mode of urban spatial expansion, strengthening the integration and potential exploitation of the land in the urban built-up area, and strengthening the control of the construction intensity of protected areas.