On the prediction of the peak overpressure of ground reflected wave using a physics-informed weighted neural network

Accurately estimating the parameters of explosion shock waves is crucial for explosion hazard assessment and blast-resistant structure design. Traditional simulation methods, such as computational fluid dynamics, can simulate the propagation process of explosion shock waves in complex environments, but they are difficult to meet the requirements of rapid assessment. Existing neural network models have demonstrated high efficiency and accuracy in overpressure prediction, but the prediction range of these models is limited by the training domain, and the generalization ability of neural network models under small sample conditions has not been verified. To overcome this limitation, this study proposes a physical information weighted neural network framework (PIWNN) based on the idea of mixture of experts. This framework consists of a physical model layer and a weight coefficient layer. Through the neural network, each physical model's predicted value is assigned a corresponding weight, and the final prediction value of the neural network is obtained by weighted summation. This model has good generalization ability and can accurately predict data outside the training domain. The PIWNN model can maintain high generalization ability under small sample test conditions, and its generalization ability is less affected by the size of the training domain. Test results on the experimental dataset show that compared with individual physical models, the prediction error MAPE of PIWNN is reduced from 17.3% to 48.1% to 11.8%, with a reduction of at least 31.7% in prediction error. The physical information neural network framework constructed in this study can provide an important reference for modeling regression problems in engineering design.