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Physics-informed neural wavefields with Gabor basis functions.

Tariq Alkhalifah1, Xinquan Huang1

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Physics-Informed Neural Networks (PINNs) struggle with wavefield complexity. This study introduces Gabor basis functions within PINNs, improving efficiency and accuracy for wave equation solutions, especially at high frequencies.

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Area of Science:

  • Computational Physics
  • Applied Mathematics
  • Machine Learning

Background:

  • Physics-Informed Neural Networks (PINNs) are powerful for solving partial differential equations (PDEs).
  • Standard PINNs face computational challenges with complex wavefield functions due to low-frequency bias in learned basis functions.
  • Polynomial-based calculations in neural networks are not inherently suited for wavefield modeling.

Purpose of the Study:

  • To enhance the efficiency and accuracy of neural network-based wavefield solutions.
  • To address the limitations of traditional PINNs in handling high-frequency wave phenomena.
  • To develop a novel PINN architecture incorporating Gabor basis functions for wave equation solutions.

Main Methods:

  • Proposed an augmentation of fully connected neural networks with an adaptable Gabor layer.
  • Modeled wavefield solutions as linear combinations of Gabor basis functions satisfying the wave equation.
  • Integrated an auxiliary network to predict Gabor function centers based on input coordinates for spatial utilization.

Main Results:

  • The proposed Gabor-enhanced PINN demonstrated superior performance compared to vanilla PINNs.
  • Significant improvements in accuracy and computational efficiency were observed, particularly for high-frequency wavefields.
  • The novel implementation effectively handled complex and realistic wave modeling scenarios.

Conclusions:

  • The integration of Gabor basis functions offers a promising approach to overcome PINN limitations in wavefield simulations.
  • This method provides a more wavefield-friendly neural network architecture, enhancing solution capabilities.
  • The Gabor-enhanced PINN is particularly effective for challenging problems involving high frequencies and intricate wave phenomena.