Efficient Prediction of Shallow-Water Acoustic Transmission Loss Using a Hybrid Variational Autoencoder–Flow Framework

Abstract

Efficient prediction of shallow-water acoustic transmission loss (TL) is crucial for underwater detection, recognition, and communication systems. Traditional physical modeling methods require repeated calculations for each new scenario in practical waveguide environments, leading to low computational efficiency. Deep learning approaches, based on data-driven principles, enable accurate input–output approximation and batch processing of large-scale datasets, significantly reducing computation time and cost. To establish a rapid prediction model mapping sound speed profiles (SSPs) to acoustic TL through controllable generation, this study proposes a hybrid framework that integrates a variational autoencoder (VAE) and a normalizing flow (Flow) through a two-stage training strategy. The VAE network is employed to learn latent representations of TL data on a low-dimensional manifold, while the Flow network is additionally used to establish a bijective mapping between the latent variables and underwater physical parameters, thereby enhancing the controllability of the generation process. Combining the trained normalizing flow with the VAE decoder could establish an end-to-end mapping from SSPs to TL. The results demonstrated that the VAE–Flow network achieved higher computational efficiency, with a computation time of 4 s for generating 1000 acoustic TL samples, versus the over 500 s required by the KRAKEN model, while preserving accuracy, with median structural similarity index measure (SSIM) values over 0.90.