Learning Acoustic Scattering in Turbulent Stratified Flows With Neural Operators

Recent advances in machine learning have demonstrated that neural networks can approximate operators using specialized architectures known as neural operators. In this work, we explore the use of Fourier Neural Operators (FNOs) to learn the physics of wave propagation in randomly layered media, mapping the space of random sound speed fields to acoustic waveforms. This approach is tested by predicting the scattering of broadband and narrowband acoustic wave packets off a stochastic gravity wave field, a key factor in atmospheric infrasound variability. Gravity wave fields are computed using a stochastic multiwave series that recovers the usual vertical wavenumber power spectral density and produces intermittency. Using spectral analysis tools, we demonstrate that FNOs can approximate physically consistent scattered pressure fields but fail to capture fine details due to the truncation of high-frequency modes in each Fourier layer. Inspired by reduced-order modeling, we propose a variant of FNOs that learns the optimal number of modes for representing the integral kernel in the Fourier layers. These modes enable the FNOs to capture intricate patterns related to the interaction between the incoming infrasound and vertically distributed small-scale structures in the sound speed profile. When applied to the inverse problem of estimating gravity wave fields from acoustic waveforms, this approach can be orders of magnitude more efficient compared to traditional finite-difference solvers.