Multiple Wavefield Solutions in Physics-Informed Neural Networks Using Latent Representation

Solutions of wave equations (e.g., wavefields) are invaluable to imaging and inverting the subsurface. The main challenge in attaining such solutions is the exponential increase in computational cost with finer discretization. Being discretization-invariant, the recently developed physics-informed neural networks (PINNs) framework offers accurate and more flexible partial differential equation (PDE) solutions than conventional solvers. However, they are challenged by the relatively slow convergence and the need to perform additional training for other PDE parameters (velocity models). To address this limitation, we introduce a PINN framework that utilizes latent representations of the PDE parameters (velocity models) as additional inputs into the PINN model and performs training over a distribution of viable velocity models. We use a two-stage training scheme in which, we first learn a latent representation for a distribution of velocity models. Then, we train a PINN 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 and benchmarking against several existing algorithms, we demonstrate that the proposed framework provides up to three times the speed up and an order of magnitude accuracy improvement. The proposed framework retains the flexibility and accuracy features of the functional representation of PINN solutions while gaining a generalization feature to adapt to various velocity models efficiently.