# Blast Loading Prediction of Complex Structures Based on Bayesian Deep Active Learning
## 1 Introduction
[14] utilized transfer learning technology, allowing the neural network to learn prior knowledge from various explosion sources. This approach facilitated the development of a high-precision blast loading prediction model with reduced training data requirements. Additionally, [PERSON] et al. [15] achieved the transformation of low-resolution data into high-resolution data using a super-resolution reconstruction method, which also helps minimize the consumption of computing resources. To highlight the significance of inputs through feature decomposition and analysis, [PERSON] et al. [16] utilized explainable artificial intelligence (XAI) in their study on blast loading prediction for rigid structures. Their research effectively predicted peak incident pressure and peak impulse using three machine learning models--decision tree, random forest, and extreme gradient boosting (XGB) types. By applying Shapley additive explanations (SHAP), the study identified key factors influencing these predictions. The results indicated that explosive mass had the greatest impact among the input parameters, aligning with fundamental blast theories. This XAI-based approach enhances understanding of the role of input information in model forecasting. Additionally, to address the blast loading prediction problem for boiling liquid expanding vapor explosions (BLEVEs), [PERSON] et al. utilized numerical simulation data generated with the commercial software FLACS. They employed a FCNN [17], integrated learning algorithms [18], transformers [19], and graph neural networks [20] to achieve relatively accurate predictions. This work advanced the research on the blast loading prediction of BLEVEs and demonstrated the effectiveness of deep learning methods in this field. Existing studies effectively predict blast loading in various scenarios by constructing different deep learning models, but they face notable limitations. These limitations stem from two key areas--the lack of uncertainty quantification and the high costs associated with model development. First, there is a lack of uncertainty quantification. Most research on blast loading prediction using deep learning relies on deterministic neural networks for point estimates, which do not quantify result uncertainty. This may lead to significant deviations from actual values [21]. Relying solely on these predictions for decision-making in pre-disaster blast-resistant design and post-disaster emergency response poses considerable risks. To evaluate the reliability of these predictions, it is essential to provide confidence information alongside blast loading estimates. Confidence measures the trustworthiness of a model or prediction, typically quantified through statistical methods; it reflects the level of trust in a result and is often associated with confidence intervals. In blast loading research, confidence intervals indicate the estimated range for predicted blast loading, while confidence denotes the probability that the interval contains the true value. High-confidence results improve decision-making effectiveness and reliability. For instance, a 95% confidence interval implies a 95% likelihood that the actual blast loading falls within that range. By quantifying uncertainty in prediction results, it is possible to demonstrate the model's confidence level, thereby increasing the reliability of the prediction methods in practical decision-making. However, research in this area remains limited. Second, the cost of model construction is high. Conventional deep learning approaches are passive, relying on all available training samples for model training. For a model to achieve high performance in predicting blast loading, a sufficient number of training samples is necessary. However, obtaining explosion data using numerical simulations can be costly, leading to high expense when developing deep learning models. In contrast, active learning [22; 23; 24; 25; 26] evaluates the value of each sample using specific data-selection strategies.