PINN-Based Seismic Wavefield Simulation With Learnable Multiscale Fourier Feature Mapping and Adaptive Activation Function

Seismic wavefield simulation is crucial for acquisition design, inversion, and interpretation in seismic exploration. The essence of seismic wavefield simulation is to solve wave equations. A physics-informed neural network (PINN) provides an alternative approach to solving partial differential equations and shows great potential for various geophysical problems. However, the accuracy of PINN-based seismic wavefield simulation is unsatisfactory due to spectral bias. Multiscale Fourier feature mapping (MFFM) has been shown to be effective in enhancing the accuracy of simulation results. This letter proposes a modified MFFM PINN for solving the Helmholtz wave equation to further improve the accuracy of seismic wavefield simulation. An auxiliary network is used to determine the initial hyperparameter value for the multiscale feature range in MFFM using the velocity model as input. The hyperparameter is fine-tuned by allowing it to be learnable during the subsequent training process of the neural network. In addition, activation functions with learnable frequencies are proposed for use in all hidden layers. Experiment results demonstrate that the proposed method automatically determines the optimal hyperparameter for accurate wavefield simulation efficiently.