## 4 Results of Numerical Simulations and Conclusions
### The Case of Having Three Scatterers  
In the case of three scatterers, as a result of learning 10,000 data, three high singular values were found as shown in Figure 11, but it can be seen that it is difficult to specify the location of the scatterers due to poor imaging results. Since further learning may lead to a risk of overfitting, the amount of data used for learning was increased. Figure 11: Singular value distribution and imaging results for output data from a model learned with 10,000 data. Figure 10: Singular value distribution and imaging result of limited-view data (top) and output data (bottom). (**a**) SVD with limited-view data; (**b**) imaging result with true data; (**c**) SVD with full-view data; (**d**) imaging result with learning data. Therefore, 100,000 data were newly created and learned again, and the previously generated 10,000 data were not used for learning but used as test data. In order to confirm that the learning progressed well, among the output full view data from the test data input into the learning model, the cases with the largest and smallest mean square errors, compared to the ground truth data, are imaged with the subspace migration algorithm in Figure 12 and Figure 13, respectively. In both cases, when imaged with ground truth data (Figures 12a and 13a) and data output through the learning model (Figures 12b and 13b), it can be seen that the positions of the three scatterers highlighted in red are the same. In addition, it can be seen that, when a singular value is calculated using this data, three relatively large singular values are detected. Therefore, it can be considered that the full view data are well constructed from the limited view data, unlike when the artificial neural network is trained using 10,000 data. Figure 12: Singular value distribution and imaging results for the case with the largest mean square error case among the test data. (**a**) SVD with true data; (**b**) imaging result with true data; (**c**) SVD with learning data; (**d**) imaging result with learning data. In addition, as in the case of two scatterers, the results of imaging the ground truth data of randomly generated scatterers and the data output by inputting this data into the learning model and the distribution of the singular value are shown in Figure 14. At this time, there are three points with large singular values in (a), (c), and (e), but in the case of limited view data, the three singular values are smaller than in other cases, so, when imaging, the location of the scatterers could not be found as shown in (b). However, when imaging with full view data output from the learning model, the locations of the scatterers could be found as shown in (f), and it was similar to the imaging result with actual ground truth data in (d). In other words, when arbitrary data that was not used at all for learning was input and imaged as output data, the locations of the scatterers could be found well. Therefore, even though the number of scatterers is three, it can be confirmed that the developed artificial neural network model has been successfully trained to construct the full-view data from the limited-view data input. Figure 13: Singular value distribution and imaging results for the case with the smallest mean square error case among the test data. (**a**) SVD with true data; (**b**) imaging result with true data; (**c**) SVD with learning data; (**d**) imaging result with learning data. The fundamental problem with the inverse scattering problem in limited view situations is that it is sometimes impossible to locate the scatterers when imaging with limited view data due to insufficient data. Through previous experiments, it was found that this problem can be solved to some extent using artificial intelligence. Based on this study, we can draw the following conclusions. Figure 14: Imaging result and singular value distribution for limited view data (top), ground truth data (middle), output data (bottom).