Hybrid operator learning of wave scattering maps in high-contrast media

TL;DR

This paper introduces a hybrid neural operator architecture combining Fourier Neural Operators and vision transformers to accurately model wave scattering in high-contrast media, improving seismic imaging simulations.

Contribution

The paper presents a novel hybrid neural operator that decomposes wave scattering into background and high-contrast components, enhancing modeling accuracy in challenging media.

Findings

Significantly improved phase and amplitude accuracy over standalone models

Effective modeling of high-frequency Helmholtz problems with strong contrasts

Favorable accuracy-parameter scaling in high-contrast wave scattering simulations

Abstract

Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as seismic imaging and inversion. High-contrast settings, such as subsurface models with salt bodies, exhibit strong scattering and phase sensitivity that challenge existing neural operators. We propose a hybrid architecture that decomposes the scattering operator into two separate contributions: a smooth background propagation and a high-contrast scattering correction. The smooth component is learned with a Fourier Neural Operator (FNO), which produces globally coupled feature tokens encoding background wave propagation; these tokens are then passed to a vision transformer, where attention is used to model the high-contrast scattering correction dominated by strong, spatial interactions. Evaluated on high-frequency Helmholtz problems with strong contrasts, the hybrid model achieves substantially improved phase and amplitude accuracy compared to standalone FNOs or transformers, with favorable accuracy-parameter scaling.