## 4 Results
### Population Spatialization Result Validation and Error Analysis  
In this study, we use the random forest regression model obtained with the Bayesian optimization based on gradient boosting regression to spatialize the population of Sichuan Province in 2020, and obtain a 1 km grid population distribution map of Sichuan Province (Figure 16). From the map, it is evident that the population in Sichuan Province is primarily concentrated in the eastern Chengdu Plain and various urban centers. There is a noticeable trend of population density decreasing gradually from the urban centers towards the surrounding areas. In the western Qinghai-Tibet Plateau region, the population is sparse, with only a few areas having small populations. This distribution aligns closely with the actual population distribution in Sichuan Province. This indicates that the population spatialization model proposed in this article is effective. This study's population spatialization model was trained using county-level administrative population census data. In order to validate the accuracy of population distribution at smaller spatial scales after gridification, we selected the seventh national population census data at the township level, which is smaller than the county-level administrative division, as the validation dataset. We also conducted an analysis of areas with significant errors to provide insights for future research. Due to limited access to township-level census data, we collected population data for 2122 townships and streets. In areas where population census data was missing, we used gridded population data as a base map. Then, we count the populations of the 2122 townships based on the RF-BOA Population Map, and compare them with the data collected from the seventh national population census. The evaluation of the results was conducted using the Relative Error (RE), which was calculated using Formulas (10) and (11) below. The error distribution chart was also created, as depicted in Figure 17.  
\[E=Pop_{pred}-Pop_{true}, \tag{10}\]\[RE=\frac{E}{Pop_{true}} \tag{11}\]  
In Formulas (10) and (11), \(Pop_{pred}\) is the predicted population of townships obtained in this study, \(Pop_{true}\) corresponds to the actual population of townships obtained from the population census, and \(E\) is the difference between the predicted population and the actual population. Figure 17 illustrates the spatial distribution of relative errors in the population dataset for Sichuan Province created in this study. As depicted in the figure, the relative errors in the population distribution of around 70% of townships and streets are relatively small, while approximately 3% of townships and streets exhibit larger errors. These larger errors are scattered across the region and do not exhibit a specific spatial pattern. This phenomenon suggests that the gridding model proposed in this paper has a strong spatialization capability at the township level, accurately capturing population distribution. The model is effective in fine-grained population distribution. Figure 16: The population distribution map with 1 km resolution of Sichuan Province (RF-BOA Population Map). Figure 17: Spatial analysis of relative error. To further investigate the causes of prediction errors in the model, the article selected two townships (Shenguozhuang Township and Renli Town) with the highest relative errors as validation areas. The relative error of population distribution in townships and streets in the verification area was analyzed combined with land cover data, satellite images of Google Maps in 2020, and POI data. Figure 17a,b show that both townships have a predominant land cover of shrubland, forests, and cultivated land, with a high vegetation cover. The satellite imagery reveals minimal human activities, such as building structures, road networks, transportation, and public facilities. Only Renli Town has a few POI data points.