Physics-informed machine learning for matched field source-range estimation

A physics-informed machine learning (ML) framework for ocean acoustic source localization using matched field processing (MFP) is presented. A physics-informed neural network (PINN) predicts complex acoustic pressure fields from sparse pressure measurements and a known sound speed profile (SSP). These PINN-predicted replica fields are integrated into the MFP scheme, enabling fine-resolution source–receiver range estimation without requiring detailed geoacoustic bottom parameters. Validation with experimental data from the Shallow Water Evaluation Cell Experiment 1996 (SWellEx-96) demonstrates accurate range estimation, including in the challenging closest point of approach region. The method maintains performance when localizing from array element depths excluded during PINN training and under sparse-array configurations and moderate SSP mismatch. Compared to conventional model-based MFP, the method avoids full environmental characterization and mitigates environmental mismatch effects. Unlike purely data-driven ML methods, it incorporates the governing wave physics, producing physically consistent replicas and improving interpolation/extrapolation to ranges and array element depths that were not used in training. These results highlight the advantages of a physics-informed data-driven approach for ocean acoustic localization in realistic, data-limited environments.