## 5 Conclusions  
Based on the analysis of the spatiotemporal distribution of heavy rain and the characteristics of disaster occurrence in the Beijing-Tianjin-Hebei region, this paper selected ten heavy rain disaster risk factors from four dimensions of regional heavy rain disaster factors, disaster-breeding environment, disaster-bearing bodies, and disaster mitigation capacity to construct a disaster risk assessment model by using daily scale precipitation data, heavy rain historical disaster data, and social and economic data of 26 meteorological observation stations in the region. The application of the MAML meta-learning method in the hyper-parameter optimization of the random forest model was improved, so as to construct the MAML-RF assessment model, and the accuracy was compared with the SCV -RF model based on traditional random search and cross validation hyper-parameter optimization. The more accurate mode was selected to evaluate the heavy rain disaster risk in the region, the SHAP interpretability algorithm was introduced to quantify the impact of each risk factor, and risk assessment was carried out for the typical year of regional heavy rain disaster.  
The results show the following outcomes:  
1. The number of heavy rain days and the annual characteristics of heavy rain show a downward trend, but a significant upward trend from 2000 to 2017.
2. The MAML-RF model improved simulation accuracy, precision, and recall by 4.44%, 3.71%, and 4.44%, respectively, over the SCV-RF model, while also reducing simulation time by 2.06 s. This indicates that the improved MAML-RF model provides superior output results in assessing heavy rain disaster risk, demonstrating high robustness and generalization capability.  
3. The introduction of the SHAP interpretability algorithm for analyzing the MAML-RF model revealed that five heavy rain disaster risk factors--number of heavy rain days, rainfall amount, slope, drainage pipe density, and impervious surface ratio--have the most significant impact on disaster risk. The driving effect of these disaster-inducing factors on heavy rain disaster risk is more pronounced compared to the disaster-prone environment, disaster-bearing body, and disaster mitigation capacity, with a cumulative influence weight reaching 0.519.
4. The spatiotemporal distribution of heavy rain disaster risk has exhibited significant changes. The area of high-risk within the region has increased. Relatively high-risk and high-risk areas are mainly distributed in the south-central part of Beijing, southern Hebei Province cities such as Shijiazhuang, Hengshui, and Xingtai, eastern Hebei cities like Chengde and Qinhuangdao, and southern Tianjin. The area proportion of medium-risk zones to the area remains relatively stable. Low-risk areas for the disaster are clustered in the northwestern plateau area.  
Conceptualization, Y.F. and Y.W.; methodology, Y.F.; software, Y.F.; validation, Y.F.; formal analysis, Y.F.; investigation, Y.W.; resources, Y.F.; data curation, Y.F.; writing--original draft preparation, Y.F.; writing--review and editing, Y.F. and Y.W.; visualization, Y.F.; supervision, Y.W.; funding acquisition, W.X. and B.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Project (2023 YFC3205701) and Guangdong Foundation for Program of Science and Technology Research (2023B0202030001).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The author would like to acknowledge the research group members and [PERSON] for their assistance with manuscript preparation.  
The authors declare no conflicts of interest.