Deep neural networks for waves assisted by the Wiener-Hopf method.

Area of Science:

• Computational Physics
• Applied Mathematics
• Artificial Intelligence

Background:

• The Wiener-Hopf method is a powerful analytical technique for solving wave propagation problems.
• Deep neural networks (DNNs) require extensive datasets for effective training, often posing a challenge in physics and engineering.
• Integrating analytical methods with DNNs offers a promising avenue for data generation and model interpretability.

Purpose of the Study:

• To combine the analytical Wiener-Hopf method with deep neural networks (DNNs) for wave problem analysis.
• To leverage the Wiener-Hopf method for generating large datasets to train DNNs.
• To explore the potential of DNNs in modeling wave equations and understanding underlying physical mechanisms.

Main Methods:

• A deep feed-forward network was employed to model the forward propagation in duct acoustics.
• A convolutional U-net architecture was developed to learn spatial derivatives in wave equations.
• Extensions to the U-net were proposed to incorporate physical constraints.
• The Wiener-Hopf method was used to generate analytical solutions for training and validation.

Main Results:

• The hybrid approach successfully trained DNNs using data generated by the Wiener-Hopf method.
• The U-net architecture demonstrated capability in learning spatial derivatives for wave equations.
• Proposed U-net extensions helped in imposing physical constraints on the models.
• Neural network performance was validated against accurate analytical solutions.

Conclusions:

• The integration of the Wiener-Hopf method and DNNs provides a novel and efficient strategy for studying wave problems.
• This combinational approach enhances data generation for AI models and offers insights into physical mechanisms.
• The developed methods have potential applications in aerospace engineering, such as aeroengine noise analysis, and advance computational paradigms in physics and engineering.