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A parabolic equation-based physics-informed machine learning method for underwater sound propagation modelinga).

Ziwei Huang1, Liang An1, Yang Ye1

  • 1Key Laboratory of Underwater Acoustic Signal Processing (Southeast University), Ministry of Education, Nanjing, 210096, China.

The Journal of the Acoustical Society of America
|January 29, 2026
PubMed
Summary

U-PARANET, a new physics-informed neural network, accurately models long-range underwater sound propagation by integrating the parabolic equation. This method improves stability and reduces errors for ocean monitoring and communication applications.

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Area of Science:

  • Ocean acoustics
  • Underwater physics
  • Machine learning applications

Background:

  • Traditional underwater sound propagation models face computational and adaptability limits.
  • Data-driven methods lack physical constraints and require large datasets.
  • Physics-Informed Neural Networks struggle with accurate long-range extrapolation.

Purpose of the Study:

  • To develop a physics-informed machine learning method for accurate long-range underwater sound propagation modeling.
  • To enhance the stability and reduce error accumulation in acoustic propagation predictions.
  • To improve underwater environmental monitoring, communication, and localization.

Main Methods:

  • Proposed U-PARANET, a physics-informed machine learning model.
  • Incorporated the parabolic equation as a hard constraint within the neural network architecture.
  • Leveraged the parabolic equation's recursive structure for enhanced stability.

Main Results:

  • U-PARANET accurately predicted transmission loss and phase structures in simulated and experimental data.
  • Achieved low mean absolute errors for transmission loss: 1.40 dB (ideal), 1.06 dB (simulated SWellEx-96), and 2.87 dB (experimental SWellEx-96).
  • Demonstrated good agreement in spatial field patterns and robust long-range extrapolation.

Conclusions:

  • U-PARANET exhibits excellent long-range underwater sound propagation modeling capabilities.
  • The method shows robust extrapolation in challenging, realistic ocean environments.
  • U-PARANET offers a promising advancement for oceanographic applications.