GaborPINN: Efficient physics informed neural networks using multiplicative filtered networks
This work addresses a bottleneck in computational geophysics for applications like full waveform inversion, though it is an incremental improvement over existing PINN methods.
The authors tackled the slow convergence of physics-informed neural networks (PINNs) for solving the Helmholtz equation in seismic wavefield computation by proposing GaborPINN, which uses multiplicative filtered networks with Gabor basis functions and prior frequency information, achieving up to a two-magnitude increase in convergence speed compared to conventional PINNs.
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.