PINNup: Robust Neural Network Wavefield Solutions Using Frequency Upscaling and Neuron Splitting

Seismic wave-equation based methods, for example, full waveform inversion, are currently used to illuminate the interior of Earth. Solving for the frequency-domain scattered wavefield via physics-informed neural network (PINN) has great potential in increasing the flexibility and reducing the computational cost of seismic modeling and inversion. However, when dealing with high-frequency wavefields using PINN, its accuracy and training cost limit its application. Thus, we propose a novel implementation of PINN using frequency upscaling and neuron splitting, which allows the neural network model to grow in size as we increase the frequency while leveraging the information from the pre-trained model for lower-frequency wavefields, resulting in fast convergence to highly accurate wavefield solutions. Numerical results show that, compared to the commonly used PINN with random initialization, the proposed PINN exhibits notable superiority in terms of convergence and accuracy and can achieve neuron based high-frequency wavefield solutions with a shallow model.