In the domain of flood forecasting, machine learning models have been increasingly adopted to enhance prediction accuracy. Recent systematic reviews have highlighted the significant potential of machine learning applications in disaster management, particularly emphasizing improvements in flood prediction, risk assessment, and emergency response [26]. Several studies have summarized various machine learning techniques, discussing their strengths, limitations, and proposing future research directions [27]. For instance, integrating hydrological and meteorological data within machine learning frameworks has notably improved the accuracy and real-time performance of flood forecasting systems [28]. Weather forecast-driven machine learning approaches have demonstrated strong predictive capabilities for agricultural flood prediction tasks, such as in the Yangtze River basin [29]. Additionally, combining principal component analysis with machine learning methods has facilitated spatial-temporal forecasting of flood inundation events [30, 31].

Gradient Boosting Decision Trees and Convolutional Neural Networks have been effectively employed to assess flood risks in regions like the Pearl River Delta, providing detailed analyses of critical risk factors [32]. Heterogeneous data sources integrated into machine learning models have also supported robust flood risk mapping and provided effective decision-making assistance in regions such as Xinjiang [33]. Furthermore, ensemble learning methods, including Random Forest and XGBoost, have enhanced flood susceptibility modeling and improved the precision of flood risk assessments [34]. Integrating machine learning techniques with geographic information systems has enabled accurate urban flood predictions and detailed simulation of flood dynamics across diverse urban environments [35].

Despite these advancements, current approaches often exhibit limited computational efficiency, constraining their real-time applicability in disaster response. Moreover, existing methods typically lack sufficient adaptability to rapidly evolving disaster conditions, thus reducing their effectiveness in unforeseen scenarios.

In the field of disaster management, machine learning techniques combined with remote sensing technologies have been increasingly employed to enhance emergency response efficiency. Recent studies have integrated hydrodynamic modeling with machine learning to provide robust scientific support for urban flood management [36]. Machine learning approaches have also been used to forecast the number and distribution of households affected by floods, assisting governmental authorities in developing effective rescue strategies [37]. Furthermore, social media data, such as information extracted from platforms like Weibo, have been utilized within flood risk assessment models, enabling rapid situational awareness through timely disaster-related insights [38]. Deep learning methods combined with remote sensing imagery analysis have improved the capability of assessing dynamic changes in flood disasters, particularly in accurately determining the spatial extent of flooding [39].

Additionally, global flood monitoring methods using low-cost satellites in conjunction with machine learning have significantly expanded the spatial coverage of disaster early-warning systems [40]. Ensemble learning techniques, such as Random Forest and Radial Basis Function Neural Networks, have facilitated accurate flood risk evaluations, notably improving prediction accuracy in regions like the Yangtze River Delta [41]. Machine learning has also been integrated with hydrological models to establish efficient flood forecasting methods [42]. Image processing combined with machine learning has supported rapid post-disaster damage assessment and effective recovery planning through analysis of post-event imagery data [43]. Moreover, methods incorporating Random Forest and Support Vector Machines have effectively identified high-risk flood-prone areas, enhancing preparedness and mitigation strategies [44]. A Bayesian convolutional neural network was developed for predicting urban flood inundation, showcasing high accuracy and uncertainty quantification for real-time flood forecasting [45].

However, despite their effectiveness, existing approaches often rely heavily on historical data patterns, thus limiting their predictive capability in unprecedented disaster scenarios. Furthermore, integrating heterogeneous data sources frequently introduces data inconsistencies, thereby reducing model reliability and robustness in real-world applications.

The fundamental idea underlying BDNNs is treating network parameters, including weights and biases, as probabilistic random variables instead of deterministic constants. Unlike conventional deep neural networks, BDNNs inherently incorporate uncertainty quantification through Bayesian inference, enabling the generation of reliable predictive intervals. Given a dataset D={(xi,yi)}i=1N and network parameters W, the objective of BDNNs is to estimate the posterior distribution of parameters p(W|D):

where p(W|D) represents the posterior distribution of network parameters after observing the data, p(D|W) is the likelihood function describing the probability of observing the data set D given parameters W, p(W) denotes the prior distribution reflecting initial beliefs about parameters, and p(D) is the evidence serving as a normalization constant:

Due to the complexity of directly computing this integral, approximate inference methods are commonly adopted in practice.

Bayesian inference provides the fundamental computational framework for BDNNs by systematically updating the probability distribution of network parameters based on observed data. Specifically, the posterior distribution of the parameters p(W|D) can be formally represented using Bayes' theorem as:

However, direct analytical computation of this posterior distribution is typically intractable due to the high dimensionality and complexity of the integral involved, as illustrated in Figure 1. To address this computational challenge, we employ VI as an approximation strategy, introducing a tractable variational distribution q(W|θ) with variational parameters θ to approximate the true posterior p(W|D).

Figure 1 visually illustrates the process of Bayesian inference in BDNNs, clearly showing the relationships between the prior distribution p(W), the true posterior distribution p(W|D), and the variational approximation q(W|θ). Specifically, the prior distribution p(W) expresses initial assumptions about the parameters before data observation. The true posterior distribution p(W|D), usually complex and intractable, represents the updated beliefs about the parameters after data has been observed. The variational distribution q(W|θ) is introduced as a simplified, computationally feasible distribution used to closely approximate the true posterior, effectively transforming the complex integral computation into a manageable optimization problem.

Due to the intractability of the true posterior distribution p(W|D), Variational Inference seeks a variational distribution q(W|θ) parameterized by θ to approximate the true posterior. Specifically, the objective of VI is to minimize the Kullback-Leibler (KL) divergence between the approximate and true posterior:

This KL divergence can be expanded explicitly as:

To simplify the optimization, the Evidence Lower Bound (ELBO) is maximized instead:

Here, the first term represents the expected log-likelihood under the variational distribution, while the second term regularizes the approximation toward the prior distribution.

To quantify predictive uncertainty, MC sampling is applied, which involves drawing multiple parameter samples from the variational posterior distribution q(W|θ):

For a new input data point x, the predictive mean y_pred is computed by averaging predictions from these sampled parameters:

Additionally, predictive uncertainty is measured through the variance of these sampled predictions, calculated as:

Here, a higher variance indicates greater uncertainty regarding the prediction.

The proposed BDNN architecture consists of several key components illustrated in Figure 2. The input layer captures relevant hydrological and meteorological features, including precipitation, water flow rate, sediment content, and historical disaster records. Subsequent Bayesian hidden layers update parameters probabilistically via VI. Each hidden layer's activation h_i is computed as:

where σ(·) is the activation function, and L represents the total number of hidden layers.

MC Dropout layers are strategically incorporated to improve generalization and prevent overfitting, defined by:

Here, m_i is a Bernoulli mask vector, and p is the dropout probability.

A Hierarchical Attention Mechanism dynamically focuses on the most informative features, with attention weights α_j calculated as:

where W_a, b_a, v are learnable parameters within the attention module.

Finally, the Bayesian output layer produces predictions accompanied by uncertainty estimation. Predictions for the output layer are calculated by:

Predicted means and variances for output are again computed using the Monte Carlo samples from the posterior distribution. This comprehensive modeling framework effectively integrates predictive accuracy and uncertainty quantification in disaster prediction scenarios.

The dataset used in this study was collected from various hydrological monitoring stations across the Yellow River basin, covering the period from 2001 to 2023. It consists of ~10,000 records that include daily measurements of variables such as annual precipitation, precipitation compared to the previous year, river channel gradient, initial precipitation, sediment storage, flood conditions, dredging activities, risk assessment indicators for rivers and dams, and actual flood occurrence status. These data provide rich information for model training and lay a solid foundation for model evaluation and validation. The selection and consideration of data are based on data availability, quality, and multi-source data integration to ensure the improvement of model prediction performance. A snapshot of the original dataset is shown in Figure 3.

The feature set selected in this study, including hydrological measurements such as annual precipitation, initial precipitation level, sediment storage, and categorical variables such as flood severity, risk management measures, and historical occurrence data, is based on an in-depth analysis of flood occurrence mechanisms and a comprehensive consideration of relevant literature. These features are closely related to the key drivers of floods and can fully capture the complexity and diversity of flood occurrence. Annual precipitation is directly related to flood occurrence, initial precipitation level reflects the wetness of the basin, and sediment storage affects river mobility. Categorical variables such as flood severity and risk management measures provide historical context and human intervention information for flood events. Historical flood data further helps the model identify the periodicity and trend of flood occurrence. The selection of these features not only ensures that the model can understand flood risks from multiple perspectives, but also takes into account the availability and quality of data, providing a solid foundation for the accuracy and reliability of the model. Through this feature selection process, we have built a comprehensive and representative database, which provides strong data support for the training and validation of flood prediction models.

Data preprocessing was essential to improve data quality and optimize model training efficiency. Initial steps included removing duplicate records and handling missing values; numerical missing values were imputed using interpolation or mean values, while categorical variables were imputed using the most frequent category, both are simple, efficient and can better reflect the data distribution characteristics. In addition, the robustness of the BDNN model reduces the need for complex interpolation methods. In contrast, k-NN interpolation is computationally complex and has limited effectiveness in high-dimensional data, while multiple interpolation is complex to implement and increases training costs. Furthermore, numerical features were standardized using Z-score normalization to ensure stable training processes. Categorical variables were transformed via one-hot encoding for effective integration into the machine learning models. An example of the dataset after these preprocessing steps is shown in Figure 4.

To optimize feature selection and enhance model efficiency, we analyzed feature correlations using a heatmap (Figure 5). The analysis revealed strong positive correlations, notably between annual precipitation and initial precipitation, and between condition probability and actual flood occurrence. Conversely, some negative correlations emerged, such as between severe flood conditions and actual flood occurrences, likely due to effective regional flood mitigation measures. Features such as channel gradient exhibited minimal correlation, suggesting indirect impacts on flood risk.

Based on these insights, we removed redundant or weakly correlated features to streamline the dataset. Key influential variables–including annual precipitation, solid material storage, condition probability, and flood conditions–were retained to ensure accurate predictions. Additionally, interaction analysis was conducted by combining critical features (e.g., precipitation levels and dam risk ratings), further improving model effectiveness in complex scenarios.

Experiments were conducted on a high-performance computing platform equipped with an Intel Core i7-9700H CPU and an NVIDIA GeForce GTX 1660 Ti GPU. We employed Python along with PyTorch as the primary deep learning framework. The dataset was randomly partitioned into training (80%) and testing sets (20%). During model training, we applied the Adam optimizer with a learning rate of 0.01 and conducted training for 1,000 epochs with a batch size of 64. To mitigate overfitting and enhance model generalization, a dropout rate of 0.5 was incorporated into the training process. Hyperparameters were determined through preliminary experimentation to balance computational efficiency and predictive performance. In order to strictly evaluate the generalization ability and reliability of the model, the construction of the prediction dataset follows the data source consistent with the training data, temporal independence, diverse scenarios, and strict data quality control to ensure that the prediction performance of the model under different conditions is comprehensively evaluated.

We rigorously evaluate the reliability and predictive performance of our model on independent forecasting datasets, using a range of established performance metrics including accuracy, precision, recall, and F1 score. This multifaceted evaluation provides us with a comprehensive understanding of the strengths and limitations of our model in real-world forecasting scenarios. Accuracy measures the correctness of the predictions overall, while precision and recall are critical for evaluating performance on imbalanced datasets commonly found in disaster forecasting scenarios. The F1 score was chosen to provide a balanced metric that considers both precision and recall, suitable for a balanced assessment of false positives and false negatives in flood forecasting tasks.

To evaluate the effectiveness of the proposed BDNN in flood prediction, we compared its performance against several traditional machine learning methods including Random Forest, XGBoost, SVM, and MLP. The evaluation metrics used were accuracy, precision, recall, and F1 score.

As shown in Table 1 and Figure 6, the proposed BDNN model consistently outperformed traditional methods across all evaluation metrics. Specifically, BDNN achieved the highest accuracy of 94.6%, representing an improvement of 4.2 percentage points over the second-best MLP model (90.4%), and significantly outperforming baseline models such as XGBoost (83.5%) and Random Forest (82.3%). Moreover, BDNN exhibited superior precision (95.2%) and recall (94.1%), demonstrating its strong ability to minimize false alarms and accurately capture actual flood occurrences. These results underscore the effectiveness, reliability, and practical utility of the BDNN model for flood prediction tasks.

To further assess the contributions of individual model components, we conducted a series of ablation studies by systematically removing key modules from the BDNN model: VI, MC Dropout and the Hierarchical Attention Mechanism. The performance results for each model variant are presented in Table 2.

The ablation results indicated that each component significantly contributes to overall model performance. Removing the Hierarchical Attention Mechanism resulted in the most substantial performance decrease, with accuracy dropping by 4.6%, underscoring its critical role in effective feature selection and prediction accuracy enhancement. Similarly, the removal of VI and MC Dropout reduced accuracy by 2.4 and 2.0%, respectively, emphasizing their importance in improving generalization and reliability. When both VI and MC Dropout were removed simultaneously, accuracy further declined to 91.0%, highlighting the synergistic effects of these components in maintaining model stability and prediction reliability. Thus, our comprehensive BDNN model, integrating all modules, achieved optimal performance.

To further analyze the predictive capability of the model across different sample types, we plotted the density distribution curves of predicted probabilities as shown in Figure 7. The horizontal axis represents the predicted probability, and the vertical axis denotes the probability density, differentiating between actual flood occurrences (Happened) and non-occurrences (Did Not Happen).

Figure 7 shows that the predicted probabilities for both classes cluster tightly in the 0.89–0.91 range, with flood events peaking slightly higher (0.90) than non-flood events. This indicates that the model is highly confident for most samples and that an alarm threshold near 0.90 would maximize recall, ensuring that the vast majority of true floods are captured. The shoulder at 0.85–0.89 corresponds to lower-confidence cases: here the model occasionally overestimates risk, so analyst review or additional data may be warranted. Minor ripples around 0.88 likely stem from measurement noise or stochastic variability in the Bayesian ensemble. Although overall calibration is good, fine-tuning the decision threshold or enhancing the uncertainty module could further reduce false alarms without sacrificing detection performance.

We further examined the prediction uncertainty of the model. The horizontal axis represents predicted probability values, and the vertical axis shows the number of samples within each probability interval, combined with a smooth probability density estimate curve.

Figure 8 reveals that 84 % of all predictions fall within the high-confidence band 0.85–0.95, peaking at 0.90; these cases can safely trigger automatic alerts because the model's uncertainty is minimal. By contrast, the lower tail (0.80–0.85) contains comparatively few samples but exhibits the largest predictive variance, reflecting ambiguous class boundaries or anomalous patterns; we therefore recommend manual verification for this band before issuing warnings. The upper tail (>0.95) often corresponds to multi-day flood sequences in which successive forecasts remain extremely confident; to avoid alarm fatigue, duplicate alerts can be consolidated and operational resources redirected toward on-the-ground response. Overall, while the distribution confirms strong model reliability, future work on feature engineering, data augmentation, and architecture refinement could further compress the tails and bolster robustness.

To validate the robustness of the proposed model under various perturbations, we conducted systematic robustness tests by adding different levels of random noise to the input data and adjusting the dropout rates to simulate variations encountered in practical scenarios. The results are presented in Table 3.

The robustness experiments showed that the model's accuracy slightly decreased to 93.5% when noise at a level of 0.1 was added, demonstrating strong resilience to minor data disturbances. Increasing the noise level further to 0.2 resulted in accuracy dropping to 92.0%, though performance remained relatively high. Similarly, adjustments to the dropout rate (0.3 and 0.4) resulted in accuracy levels of 93.0% and 91.5%, respectively, indicating the model's resilience to training randomness.

Overall, these experiments confirmed that the proposed BDNN model maintains excellent stability and generalization performance under data perturbations and training variability. Nonetheless, performance declines under more extreme perturbations highlight opportunities for future research into advanced training strategies or model refinements to enhance real-world applicability and reliability.