On the use of neural networks for full waveform inversion

Neural networks have recently gained attention in the context of solving inverse problems. Physics-Informed Neural Networks (PINNs) are a prominent methodology for the task of solving both forward and inverse problems. In the paper at hand, full waveform inversion is the inverse problem under consideration. The performance of PINNs is compared against classical adjoint optimization. The comparison focuses on three key aspects: the forward-solver, the representation of the material, and the sensitivity computation for the gradient-based minimization. Starting from PINNs, each of these key aspects is investigated and adapted individually until the classical adjoint optimization emerges. It is shown that it is beneficial to use the neural network only for the discretization of the unknown spatially varying material field. Here the neural network produces reconstructions without oscillatory artifacts as typically encountered in classical full waveform inversion approaches. Due to this finding, a hybrid method is proposed. It exploits both the efficient gradient computation with the continuous adjoint method as well as the neural network ansatz for the unknown material field. This new hybrid method outperforms Physics-Informed Neural Networks and the classical adjoint optimization in two-dimensional and three-dimensional settings.