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.

翻译：神经网络近年来在解决反演问题方面引起了广泛关注。其中一种突出的方法是物理信息神经网络（PINNs），它能够同时解决正演和反演问题。本文以全波形反演为研究目标，将PINNs的性能与传统伴随优化方法进行对比，重点关注三个关键方面：正向求解器、反演场的神经网络假设形式，以及基于梯度优化的灵敏度计算。从PINNs出发，我们逐步调整每个关键方面，直至衍生出经典伴随优化方法。研究表明，仅将神经网络用于未知材料场的离散化是有益的，因为神经网络能产生无振荡伪影的重建结果，而这类伪影在经典全波形反演方法中普遍存在。基于这一发现，我们提出了一种混合方法，该方法同时利用了连续伴随方法的高效梯度计算优势和未知材料场的神经网络假设形式。在二维和三维示例场景中，这种新型混合方法的表现优于物理信息神经网络和经典伴随优化方法。