GaborPINN: Efficient physics informed neural networks using multiplicative filtered networks

TL;DR

The paper tackles the slow convergence of physics-informed neural networks (PINNs) for frequency-domain seismic wavefields governed by the Helmholtz equation. It introduces GaborPINN, which embeds wavefield structure via multiplicative filtered networks (MFN) that use a Gabor basis, with filter frequencies tied to the target frequency to improve convergence. Key contributions include the formulation of an MFN-based PINN with a GaborNet, a regularization strategy to avoid trivial solutions, and a thorough demonstration that GaborPINN converges up to two orders of magnitude faster than vanilla PINNs on Marmousi-like models and at higher frequencies. The work highlights the importance of carefully initializing the frequency scale to balance smoothness and detail, offering a practical path toward efficient, frequency-aware PINN-based seismic wavefield representations for applications like full waveform inversion.

Abstract

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.

Figures (8)

• Figure 1: The GaborPINN framework for seismic wavefield simulation.
• Figure 2: True velocity (a); the real (b) and imaginary (c) parts of the 4 Hz scattered wavefield calculated numerically.
• Figure 3: The Loss curves for three versions of PINNs.
• Figure 4: The real-part predictions of the 4Hz wavefield due to a source near the surface at 1.25 km at various epochs (b-m) for three versions of PINNs. (b-e) are the results for the MLP comprised of 3 hidden layers with 256 neurons in each layer, (f-i) are the MLP comprised of 3 hidden layers with 512 neurons in each layer, and (j-m) are the results of GaborPINN.
• Figure 5: The prediction results (a-d) of GaborPINN with different initial frequency scales applied to testing points $\mathbf{x}_{test}$, which are perturbed compared to the training points $\mathbf{x}_{train}$, and that of GaborNet whose scale is 256 (e) evaluated at the training points $\mathbf{x}_{train}$.