Advantages and promises of deep neural operators for the prediction of wave propagation

Physics-based deep learning experienced a major breakthrough a few years ago with the advent of neural operators. Beyond the traditional use of deep neural networks to predict the solution to a fixed Partial Differential Equation (PDE), these novel methods are able to learn the operator solution to a class of PDEs.

Comparisons and analyses of popular neural operators such as Fourier Neural Operator and DeepONet have been conducted for numerical case studies. However, they are still lacking for more realistic problems in complex settings.

In this study, we compare several neural operators to predict the propagation of seismic waves in heterogeneous media. Our database is composed of more than 12 million ground motion timeseries generated from 50,000 media. We quantify the accuracy of the neural operators, their memory requirements, and their dependence towards both the initial condition and the PDE parameters. We also propose insights on their possible extension to 3 dimensions.