3D elastic wave propagation with a Factorized Fourier Neural Operator (F-FNO)

Abstract

Numerical simulations are computationally demanding in three-dimensional (3D) settings but they are often required to accurately represent physical phenomena. Neural operators have emerged as powerful surrogate models to alleviate the computational costs of simulations. However, neural operators applications in 3D remain sparse, mainly due to the difficulty of obtaining training databases for supervised learning and the size of 3D neural operators that poses memory challenges.This work focuses on the propagation of elastic waves in 3D domains and showcases the Factorized Fourier Neural Operator (F-FNO) as an efficient and accurate surrogate model. The F-FNO is trained on the publicly available HEMEW-3D database of 30 000 wavefields simulations in realistic heterogeneous domains. The F-FNO predicts space- and time-dependent (3D) surface wavefields depending on the characteristics of the propagation domain (characterized by the velocity of shear waves). Four FNO variants are compared and extensive investigations on the influence of hyperparameters and training strategies are conducted.The two most influential hyperparameters are the number of layers and the number of channels, meaning that richer models are more accurate. On the contrary, increasing the number of Fourier modes had little influence and did not reduce the spectral bias that causes an underestimation of high-frequency patterns. The F-FNO is sensitive to heterogeneities in the inputs but robust to the addition of noise. Additionally, it possesses good generalization ability to out-of-distribution data and transfer learning is very beneficial to improve the predictions in tailored applications.