Matched-field source-range estimation with physics-informed machine learning

We present a physics-informed machine learning framework for matched-field processing (MFP) to estimate source–receiver range in ocean acoustic environments. The approach employs a physics-informed neural network (PINN) trained on sparse acoustic pressure measurements and a known sound speed profile. Matched-field range estimation is performed by comparing measured pressure data with replica fields computed at multiple candidate source–receiver ranges. The estimated range is identified as the position that maximizes a match function (e.g., the Bartlett processor). Conventional MFP generates replica fields using numerical acoustic propagation models, which require detailed knowledge of the ocean environment, including bottom properties. In contrast, our method generates replica fields by predicting pressure fields at the receiver location across multiple candidate source–receiver ranges. The PINN-generated replica fields remove the need for explicit bottom modeling. Instead, the PINN implicitly learns environmental propagation effects from the training data. To ensure physical consistency, the Helmholtz equation is enforced as a constraint during PINN training. This physics-informed-data-driven approach enables accurate source localization and holds promise for geoacoustic inversion in scenarios with only partial environmental information.