## 1 Introduction  
With the accelerating impact of climate change and urbanization, the hydrological cycle has intensified. This has led to an increase in the frequency and severity of heavy rain disasters, which cause varying degrees of damage to social life and economic development [1]. Research indicates that climate change alters the spatial distribution of disaster-prone environments, expands the influence and duration of disaster-causing factors, and consequently affects the frequency, intensity, and scale of heavy rain disasters [2]. China's \"14 th Five-Year Plan\" for disaster prevention and mitigation highlights that ongoing urbanization and industrialization, along with the rapid development of infrastructure, urban complexes, and utility networks, are increasing the exposure, concentration, and vulnerability of disaster-bearing bodies within urban agglomerations, thereby escalating the systemic and complex nature of disaster risks [3]. Moreover, under the effects of climate change and urbanization, the risk of heavy rain and flooding disasters in China is expected to intensify [4]. Commonly used methods for assessing heavy rain disaster risk include historical disaster assessment [5], the indicator system method [6; 7], the remote sensing and geographic information system (GIS)coupling method [8; 9], and scenario simulation [10]. In recent years, with the rapid development of artificial intelligence, machine learning algorithms such as neural networks, support vector machines, and gradient boosting have been widely applied in disaster risk simulation, achieving high simulation accuracy [11; 12]. Among these, the random forest (RF) algorithm is noted for its strong data mining capability, high simulation accuracy, and good tolerance to outliers and noise [13; 14; 15; 16]. It is well-suited in the classification of high-dimensional data [17], offering scalability and parallelism without easily falling into overfitting, making it one of the best algorithms available. However, the performance of the RF algorithm is significantly affected by changes in hyperparameters. The methods of traditional hyperparameter selection, such as grid search and random search, rely on exhaustive or random sampling on large training datasets to select the optimal hyperparameter combination. However, they are computationally expensive, inefficient, and prone to local optima [18; 19; 20]. To address the hyperparameter optimization issue in RF algorithms, various studies have employed hill-climbing algorithms [21], sparrow search algorithms, slime mold algorithms [22], ensemble learning algorithms [23], and Bayesian algorithms [24]. However, these algorithms are often effective only when RF models have sufficient and evenly distributed data, which may not be the case with limited sample sizes, leading to overfitting and reduced generalization ability, simulation accuracy, and stability. Model-agnostic meta-learning (MAML) is a meta-learning method that trains models across multiple tasks, using a dual-layer optimization mechanism of inner and outer loops to quickly adapt model hyperparameters to new tasks with minimal updates. Studies have shown that MAML exhibits excellent learning efficiency and generalization in few-shot learning and reinforcement learning [25]. MAML achieves meta-learning through second-order gradient computation of task loss functions on model parameters, but hyperparameter computation in RF algorithms is non-differentiable. Therefore, this study improves the application of MAML in RF algorithm hyperparameter optimization, constructing a MAML-RF model for heavy rain disaster risk assessment to enhance the generalization ability and simulation accuracy of the RF algorithm. Additionally, compared to a single decision tree, the RF algorithm has poorer interpretability, and its feature importance evaluation method may assign overly similar weights to correlated features during simulation, underestimating or unevenly distributing the influence of disaster risk factors.