## 1 Introduction  
Population spatial distribution data serves as critical geographic information, effectively aiding governmental optimization of social resource allocation, environmental management, and urban development [1; 2; 3; 4; 5]. Additionally, integrating population information with other data offers a scientific basis for risk assessment, emergency disaster response, and post-disaster reconstruction [6; 7; 8; 9; 10; 11; 12]. Traditional population data is primarily obtained through comprehensive national surveys and sampling, typically using census divisions as statistical units. However, these boundaries do not always reflect the natural distribution of data. In practical applications, there are drawbacks such as low temporal and spatial resolution, lack of support for spatial operations and analysis, and poor intuitiveness. With the support of geographic information technology, geographers enhance the study of the spatial distribution of socio-economic data by adding clear and detailed geographic references and employing spatial grid methods for quantification. This method of spatializing statistical data stores population data in a grid format, further enhancing computational efficiency and storage capacity. It promotes the integration of population statistics with other environmental data, making predictions and analyses of population-related issues more accurate. At the same time, it effectively addresses the limitations of traditional population data, improves the constraints of population census data in Earth science applications, enhances the spatial resolution of population data, and provides a more intuitive representation of spatial population distribution patterns. Traditional population spatialization methods primarily fall into two categories: spatial interpolation and statistical modeling. Spatial interpolation is a method of converting population data from a large spatial range to a small area, such as point interpolation [13] and areal interpolation [14]. These methods make the scale conversion of population data convenient but often overlook scale and boundary effects [15], leading to suboptimal performance at the boundaries of regions. Moreover, due to the presence of assumption conditions, it becomes challenging to account for spatial heterogeneity issues [16], resulting in inaccurate estimates in heterogeneous areas. The presence of outliers or extreme values can also significantly impact interpolation results, leading to inaccurate estimations. Statistical modeling methods establish population spatialization models based on the weight relationships between various auxiliary data and the spatial distribution of the population, allowing for estimates of population quantity or density in small spatial units. Compared to spatial interpolation methods, statistical models can consider the intricate relationships between various factors and population density more comprehensively, but they need to face the challenge of multi-source heterogeneous data fusion [17]. Representative methods include multiple linear regression (MLR) [18], geographically weighted regression (GWR) [19; 20], spatial lag regression model [21], kriging regression model [22], etc. Moreover, many statistical regression models are based on the assumption of linear relationships, but the distribution of populations and related factors may exhibit non-linear associations. This can lead to inaccurate modeling of the true relationships. Statistical regression models often fail to capture the complexity of geographical spatial structures, such as variations between urban centers and suburbs. This may result in models that are overly smooth in space, overlooking local variations. With the development of machine learning techniques, scholars have applied ensemble learning and neural networks to population spatialization exploration to further explore the complex relationships between multi-source geographic information and demographic statistical features.