Prior-enhanced deep learning framework for three-dimensional underwater acoustic transmission loss prediction

Three-dimensional (3D) underwater acoustic transmission loss prediction is critical for sonar operational applications and marine environmental monitoring, yet the computational cost of traditional numerical models is prohibitively high. Data-driven methods offer a promising alternative, but related research remains absent due to challenges in sample generation and high-dimensional mapping. This paper presents the first prior-enhanced deep learning framework for 3D transmission loss prediction. The framework contains three key innovations: (1) hybrid parallel computing strategy that accelerates 3D acoustic field sample generation by more than 500-fold; (2) Geo-steady field as a physical prior that converts the complex high-dimensional mapping task into a tractable fine-grained correction problem; and (3) conditional multi-scale modulation network (CMSM-Net) for adaptively mapping source parameters and sound speed profiles to the 3D acoustic field. Experiments conducted in the eastern North Pacific Ocean and the northern South China Sea show that CMSM-Net based on this framework achieves root mean square errors below 1 dB in both regions. Meanwhile, compared with Bellhop3D, CMSM-Net achieves more than three orders of magnitude of speedup for large-batch inference. This work provides a robust and efficient deep learning solution for real-time 3D underwater acoustic perception.