Wavefield solutions using a physics-informed neural network as a function of velocity

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering accurate and more flexible PDE solutions. However, they are hampered by the relatively slow convergence and the need to perform additional training for other PDE parameters. To address this limitation in wavefield simulation, we introduce a framework that utilizes latent representations of velocity models as additional inputs into PINNs and performs training over a distribution of viable velocity models. Motivated by the recent progress in generative models, we promote using autoregressive models to learn latent representations of the velocity model distribution, which act as input parameters to NN functional solutions of the wave equation. We use a two-stage training scheme in which, in the first stage, we learn the latent representations for a distribution of models. In the second stage, we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the velocity models. Through numerical tests, we demonstrate that the proposed framework retains the flexibility and accuracy features of the functional representation of PINN solutions while gaining the generalization to adapt to various velocity models.