High-Dimensional Wavefield Solutions Using Physics-Informed Neural Networks with Frequency-Extension

High-dimensional wavefield solutions, like Green’s functions, are important to waveform inversion and imaging applications. Their numerical representations often require large memory or disk space allocation, and thus, are computationally intensive to access. Physics-informed neural networks (PINNs) have shown considerable potential, as neural solvers, to add flexibility and scalability to the solution. However, when dealing with high-dimensional wavefields, their accuracy and the training cost limit their applicabilities. Thus, based on the single reference frequency loss function, we propose a PINN implementation for wavefield solutions that utilizes frequency extension and neuron splitting. As a result, the neural network model can grow in size to accommodate the increase in frequency range while leveraging the pre-trained model for the narrow frequency-range wavefield, resulting in fast convergence and high-accuracy solutions. Numerical results show that, compared to the commonly used PINN with the random initialization, the proposed PINN exhibits notable superiority in terms of convergence and accuracy.