Frequency-Domain Wave Simulation Using Physics-Informed Neural Networks (PINNs) with Free Surface Boundary Condition

Summary Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural networks (PINNs), as an effective deep learning method, have achieved successful applications in solving a wide range of partial differential equations (PDEs), although there is still room for improvement on this front. We solve the acoustic and visco-acoustic scattered-field (Lippmann-Schwinger) wave equation in the frequency domain with PINN. We propose a new hard constraint method to implement the free surface boundary conditions in the loss function of PINN. We illustrate that PINN with hard constraint has a higher accuracy than weak constraint method. We design a new neural network by adding quadratic terms. The new neural network dramatically improves the capacity and flexibility to represent complex solutions.