# Blast Loading Prediction of Complex Structures Based on Bayesian Deep Active Learning
## 1 Introduction  
When an explosion occurs, the energy from the explosive source is released rapidly in a short time, generating a high-temperature, high-pressure shock wave that interacts with surrounding structures, causing severe damage to public facilities and the environment [1, 2]. Blast loading on structures can be quantified using shockwave parameters, such as the peak overpressure at critical locations. For complex-shaped structures, calculating the blast loading is more challenging [3, 4]. To optimize the anti-explosion design of these structures across various scenarios and variables, as well as to provide critical information for emergency responses following explosion events, it is essential to predict the blast loading of complex structures quickly and reliably [5]. The integration of deep learning techniques in predicting blast loading has gained increasing attention due to their capacity to handle large datasets and model nonlinear relationships. Based on data from field tests or numerical simulations, deep-learning-based prediction models can effectively capture the complex relationships between scene parameters and shockwave parameters, allowing for rapid and accurate predictions of blast loading. Some researchers have recently studied this topic. Using numerical simulation data generated by the explosion simulator Air3D, [PERSON] et al. [6] constructed a fully connected neural network (FCNN) to predict blastloading in urban street scenes. The results indicate that for urban environments with varying street layouts and building heights, the FCNN model achieves 99.3% agreement for peak overpressure and 99.5% for pulse at key locations, demonstrating its accuracy in predicting blast loading. Additionally, based on small-scale test data, [PERSON] et al. [7] developed the FCNN model to assess blast loading for structures protected by blast wall barriers. For different wall heights, this method achieved prediction accuracies of 99.8% for peak overpressure and 99.9% for peak impulse at various locations. [PERSON] et al. [8] studied the prediction of blast loading in confined internal environments using a FCNN model. They created a 10 m \(\times\) 7 m \(\times\) 5 m cubic scenario to represent a typical internal environment and conducted 72 numerical simulations using the APOLLO blast simulator, varying the explosive yield and detonation locations. This resulted in a dataset containing 20,160 samples. The trained FCNN model achieved prediction errors within 10% for 90% of the measurement points, demonstrating its effectiveness in predicting blast loading in internal environments. To enhance the performance of deep learning models in predicting blast loading, [PERSON] et al. [9; 10; 11] employed Gaussian processes to improve the functionality of neurons in the hidden layer of a neural network. By optimizing the hidden layer's configuration using numerical simulation data or empirical modeling data, the developed radial Gaussian incremental network (RGIN) can provide more accurate predictions of blast loading in scenarios involving barrier walls. Furthermore, [PERSON] et al. [12] integrated physical principles into the loss function of the ordinary FCNN model, creating a physics-guided neural network (PGNN). This approach allows for efficient prediction of blast loading in near-field explosion scenarios. [PERSON] et al. [13] combined environmental information around the points of interest (POI) with a neural network to develop a direction-encoded neural network (DENN) for predicting blast loading in two-dimensional obstructed environments. For each POI, DENN uses the proximity of the point to its surroundings and the shortest path for the shockwave to reach the POI as inputs. By learning the underlying physical processes of shockwave propagation, the model achieves fast and accurate predictions of the peak overpressure at the POI. To reduce the computational cost of numerical simulations, [PERSON] et al.