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：最近,神经网络在解决反面问题时得到了关注。 一个突出的方法是物理化神经网络(PINNS),它可以解决前方和反面问题。在手头的纸张中,全波形反转是被视为反面的问题。PINN的性能与传统模拟优化相比较,侧重于三个关键方面:前向溶液、神经网络反向的Ansatz和基于梯度最小化的灵敏度计算。从PINNs开始,每个关键方面都单独调整,直到古典联合优化出现为止。这表明,使用神经网络只有利于使未知物质领域离散化,而神经网络在没有典型的全波形反向转换方法中通常遇到的悬浮工艺的情况下进行重建。由于这一发现,建议了一种混合方法。它既利用持续连接方法的高效梯度计算,又利用未知材料领域的神经网络Ansatz。这个新的混合方法超越了物理-内部网络和两种模式的经典同步模型。</s>