Mode-informed complex-valued neural processes for matched field processing

A complex-valued neural process method, combined with modal depth functions (MDFs) of the ocean waveguide, is proposed to reconstruct the acoustic field. Neural networks are used to describe complex Gaussian processes, modeling the distribution of the acoustic field at different depths. The network parameters are optimized through a meta-learning strategy, preventing overfitting under small sample conditions (sample size equals the number of array elements) and mitigating the slow reconstruction speed of Gaussian processes (GPs), while denoising and interpolating sparsely distributed acoustic field data, generating dense field data for virtual receiver arrays. The predicted field is then integrated with the matched field processing (MFP) method for passive source localization. Validation on the SWellEx-96 waveguide shows significant improvements in localization performance and reduces sidelobes of ambiguity surface compared to traditional MFP and GP-based MFP. Moreover, the proposed kernel based on MDFs outperforms the Gaussian kernel in describing ocean waveguide characteristics. Because of the feature representation of multi-modal mapping, this kernel enhances acoustic field prediction performance and improves the accuracy and robustness of MFP. Simulated and real data are used to verify the validity.