On the Use of Neural Networks for Full Waveform Inversion

TL;DR

This paper compares Physics-Informed Neural Networks with classical methods for full waveform inversion, proposing a hybrid approach that leverages neural networks for discretization and adjoint methods for gradient computation, resulting in improved performance.

Contribution

It introduces a hybrid inversion method combining neural networks and adjoint optimization, demonstrating superior results over existing approaches in 2D and 3D cases.

Findings

Neural networks reduce oscillatory artifacts in reconstructions.

Hybrid approach outperforms pure PINNs and classical methods.

Method effective in 2D and 3D inverse problems.

Abstract

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform inversion is the considered inverse problem. The performance of PINNs is compared against classical adjoint optimization, focusing on three key aspects: the forward-solver, the neural network Ansatz for the inverse field, and the sensitivity computation for the gradient-based minimization. Starting from PINNs, each of these key aspects is 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 material field, where the neural network produces reconstructions without oscillatory artifacts as typically encountered in classical full waveform inversion approaches. Due to this finding, a hybrid approach 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 approach outperforms Physics-Informed Neural Networks and the classical adjoint optimization in settings of two and three-dimensional examples.