GaborPINN: Efficient physics informed neural networks using
  multiplicative filtered networks
Xinquan Huang Tariq Alkhalifah
The computation of 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 functional wavefield solutions
represented by neural networks (NNs), but their convergence is 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, e.g., frequency, to achieve much faster convergence. Specifically, we
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 influence of the discontinuity of the represented
wavefield by GaborPINN. The proposed method achieves up to a two-magnitude
increase in the speed of convergence as compared with conventional PINNs.