Solution and application of two-dimensional seismic wavefield evolution based on physics-informed neural networks

Physics-Informed Neural Networks (PINN) integrate partial differential equations, initial conditions, and boundary conditions into the loss function to predict the solutions of partial differential equations, and have already demonstrated their value in solving two-dimensional (2D) seismic wavefields. However, when dealing with wave problems involving boundary conditions, the added complexity of boundary conditions can lead to imbalanced convergence rates among different loss terms, which may affect both the efficiency and accuracy of the computations. Moreover, the need to retrain the model for different problems limits the flexibility of its application. Therefore, this paper introduces an adaptive weight balancing method and presents a 2D wave simulation based on Self-Adaptive PINN (SA-PINN). This method automatically adjusts the weights in the loss function, improving the solving performance. Additionally, to improve the computational efficiency of PINN in solving similar wave problems, a transfer learning strategy is adopted. By leveraging the similarities between the PINN models of related wave problems, this strategy enhances the generalization ability of PINN when dealing with variations in source location and medium wave speed. Numerical examples in semi-infinite domains and Vshaped valleys demonstrate that this method effectively achieves intelligent and efficient simulation of 2D seismic wavefields, providing a more efficient and intelligent solution for complex seismic wave problems.