Training a deep operator network as a surrogate solver for two-dimensional parabolic-equation models.

Area of Science:

• Ocean acoustics
• Computational physics
• Applied mathematics

Background:

• Parabolic equations (PEs) are vital for modeling sound propagation in variable environments.
• Approximating the square-root operator in PEs presents a significant challenge.

Purpose of the Study:

• To train Deep operator networks (DeepONets) to approximate the parabolic equation square operator.
• To enable accurate and computationally efficient modeling of 2D sound propagation.

Main Methods:

• DeepONets were trained using sound pressure and sound speed data at various depths.
• A modified DeepONet architecture was developed to handle multiple inputs with Fourier features.

Main Results:

• The trained DeepONet accurately approximates the PE square operator for sound propagation.
• The network efficiently predicts far-field sound across diverse environmental conditions.
• The approach avoids operator approximation and complex mode trajectory calculations.

Conclusions:

• DeepONets provide an efficient and accurate method for learning complex ocean acoustic physics.
• This data-driven approach reduces computational cost in sound propagation modeling.