GaborPINN: Efficient physics informed neural networks using multiplicative filtered networks

Computing for the seismic wavefield by solving the Helmholtz equation is crucial to many practical applications, e.g., full waveform inversion. Physics-informed neural networks (PINNs) provide potential wavefield solution representations, but their convergence is very slow. To address this problem, we propose a modified PINN using multiplicative filtered networks, which embeds some of the known characteristics of the wavefield in training, to achieve much faster convergence. Specifically, we specifically use the Gabor basis function due to its proven ability to represent wavefields accurately and refer to the implementation as GaborPINN. Meanwhile, we incorporate prior information on the frequency of the wavefield into the design of the method to mitigate the problem of the continuity of the represented wavefield by these types of networks. The proposed method achieves a 2 fold increase in the speed of convergence.