Physics-informed neural operators for seismic wave propagation.

Ángel Ramos Hernández, Ivan Sanchez, Tianze Zhang, Kristopher A. Innanen

The classical numerical methods approximate the wave equation with high accuracy, however, their discrete nature creates a trade-off between resolution and computational costs, often leading to difficulties in forward modelling. To address this, data-driven deep learning approaches, such as the Fourier Neural Operators (FNO), have become popular for their ability to learn to map the wave equation. Nonetheless, the standard FNO tends to struggle with long-term predictions and suffers from spectral bias, limiting its predictive fidelity, particularly in capturing high-frequency modes of wave propagation that are a relevant component of geophysics.In this study, we investigate the applicability of Physics-Informed Neural Operators (PINO) for learning the variable-density acoustic wave equation in one dimension. PINO enhances supervised learning by incorporating a physical residual that encodes the governing physical laws, serving as a regulariser for the learned operator. In synthetic examples, PINO enhances the prediction fidelity. It reduces spectral bias relative to the standard FNO version, resulting in more accurate predictions and better capture of high-frequency content, even with limited data. These findings suggest that integrating physics directly into the operator learning process helps prevent the common failures of purely data-driven models and offers an alternative approach for seismic wave propagation.