Structural defect detection is an essential field in civil engineering. A well-known method is to emit waves to the building attached with sensors and analyze sensor signals-much like CT scan. This whole process is also known as wave inversion. However, to decode the defects from sensor signals is much time consuming and mathematically impossible, since the corresponding inverse problems are difficult to solve and usually are ill-posed in the real engineering applications. To solve these issues, data-driven approaches from deep learning have been investigated by researchers. Data-driven surrogate models like Fourier Neural Operators, DeepONets, PINNS shows strong strength in computational efficiency than the classical wave equation solvers. Additionally, a well-designed regularization networks is also able to address the ill-posedness of wave inversion. In this guided research report, we focus on building up a adversarial regularization networks which shows the capability of solving the ill-posed wave inversion. We use MINIST as an example to simulate the shape of cracks that might occur in a building. Specifically, we do a linear transformation on MINIST and add Gaussian noise as the perturbation from measurements to model the noise in collections of sensor signals in practical applications. Differents methods (no regularization, Tikhonov regularization and adversarial regualarization networks) are implemented to solve the inverse problem. Adversarial regualarization networks displays the great improvement by comparison with Tikhonov regualarization and no regualarization.