In recent years, physics-informed deep learning methods based on prior data fusion to solve forward and inverse problems based on partial differential equations (PDEs) have become a cross-disciplinary hotspot. This paper clarifies the mathematical concept and implementation of physics-informed neural networks (PINN) for the earthquake engineering numerical simulation of waves. Taking the one-dimensional fluctuation of passive term as an example, the relevant theoretical model of PINN is constructed. The feasibility of physics-driven deep learning methods in solving fluctuation problems is verified by comparing with analytical solutions and finite difference methods. The relative
\mathcalL_2 
norm errors of the wave field simulated by PINN method and other numerical algorithms are analyzed. The physical driven deep learning method combined with sparse initial wave field data formed by spectral element method is used to numerically simulate two-dimensional fluctuation problem. Typical working conditions such as free boundary conditions and undulating ground surface are realized, and the distribution characteristics of time series wave field are given. Different initial conditions are changed to test the generalization accuracy of the neural network, and a transfer learning method was proposed to significantly improve the training efficiency of the network. By using transfer learning, wave fields at different source locations in infinite media can be directly predicted with high accuracy. Comparing with the results of spectral element method, the reliability of the proposed method is verified to simulate the wave propagation of homogeneous site, spatial inhomogeneity and complex terrain site fluctuation. The results show that the physical-driven deep learning method has the advantages of meshless and fine-grained numerical simulation, and can realize the numerical simulation conditions such as free surface and side/bottom boundary wave field transmission.
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