Structural defect detection is an essential field in civil engineering. Full Waveform Inversion (FWI) has recently been further developed to address this problem by emitting waves to buildings equipped with sensors and reconstructing sensor signals, much like a CT scan. However, decoding defects from sensor signals is time-consuming and mathematically challenging, as the corresponding inverse problems are difficult to solve and often ill-posed in real engineering applications. To address these issues, researchers have investigated data-driven approaches from deep learning. Data-driven surrogate models, such as Fourier Neural Operators, DeepONets, and PINNs, demonstrate greater computational efficiency compared to classical wave equation solvers. Additionally, well-designed regularization networks can address the ill-posedness of wave inversion. Therefore, it is promising to solve the wave equation by combining surrogate models and various Machine Learning approaches. In this master's thesis, we focus on applying the DeepONets architecture to wave equations and analyzing the results obtained. Initially, we introduce various information about wave equations and traditional solvers. Moreover, we obtain our data from simulations executed on high-capacity GPU servers. Different DeepONets architectures (stacked and unstacked) with various subnetworks (FCNN, CNN) are subsequently implemented to solve the equation. Finally, each approach is evaluated, and the best one is highlighted.