Bayesian Characterization of Explosive Sources Using Fourier Neural Operators

This study focuses on the modeling and inversion of long-range acoustic propagation in vertically stratified atmospheric waveguides, where transmission loss (TL) exhibits significant variability due to small-scale structures and frequency-dependent modal behavior. We begin with a physical analysis of how TL depends on the geometry of the effective sound speed profile, emphasizing the roles of atmospheric fine structure, ducting regimes, and source frequency in shaping propagation conditions. To overcome the computational burden of traditional solvers and enable fast, uncertainty-aware inference, we develop a surrogate model based on the Fourier Neural Operator (FNO), trained to predict TL fields across a wide range of atmospheric realizations and source configurations. While FNOs are known to exhibit spectral bias and tend to underperform at high frequencies, we show that low-pass filtering of the acoustic signal does not significantly affect source energy estimation. This observation justifies the use of an FNO within a Bayesian inversion framework. Furthermore, we demonstrate that moderately small-scale atmospheric structures can be captured with sufficient accuracy to allow for systematic bias correction in the inferred yield. This strategy enables accurate and efficient Bayesian inference of source energy from filtered acoustic observations using a single FNO-based surrogate model, without the need for additional correction models.