## 4 Results and Discussion
### SDL Model Implementation on Datasets Type-2: Reflection Wave Propagation Simulation
#### 4.2.2 SDL Model Simulation for Reflected Wave Propagation with Varying Frequencies and Cycles  
To determine the effectiveness of the proposed SDL model, we have modeled the different scenarios of varying excitation frequencies and the varying number of cycles on rectangular domains with a single-point excitation source on the top edge, to simulate reflected wave propagation. These datasets are not used during the training or testing of the network. We have modeled two sets of FE simulations on the rectangular domain, first, by varying the excitation frequencies of 4 MHz, 5 MHz, and 7 MHz with two cycles of the incident wave, and, second, by modelling with three cycles using 5 MHz frequency. The FE simulations are performed using a similar approach to Section 2.3. Here, we compare the SDL modeled simulation with the FE simulation, for different scenarios. Figure 8 shows the comparison of reflected wave propagation simulation for different excitation frequencies with two-cycle signal width, and the corresponding displacement values extracted along the yellow dashed line from Figure 8 for all the frames are shown in Figure 9a,b. Similarly, Figure 10 shows the comparison of the reflection wave propagation simulation modeled using a varying number of cycles with a 5 MHz central frequency. The corresponding displacement values extracted along the yellow dashed line from Figure 10 for all the time frames are shown in Figure 11a,b. We can observe that the proposed SDL model could generate reflection wave propagation for varying frequencies and cycles. The SDL simulations are in good agreement with FE simulations. The SDL-model-based line scans follow a similar trend as the FE simulation; however, amplitude and TOF differences are present in the line scans as the future time step prediction increases. We have utilized the same metrics that we used to evaluate different geometrical boundaries predictions, and the results are illustrated in Table 3. In this case, we are comparing the MAE, RMSE, and MAPE values for two different scenarios as follows: (1) the simulation between the frequencies of 4 MHz, 5 MHz, and 7 MHz with two cycles and (2) simulation, with the number of cycles being two and three, with 5 MHz frequency. We can notice the following conclusion from Table 3: (1) with an increase in the excitation frequencies other than the training frequency, the MAE, RMSE, and MAPE values increase, but the overall magnitude is in the order of \(10^{-2}\) for MAE and \(10^{-1}\) for RMSE, while the maximum MAPE is 221% on amplitude. (2) Increasing the number of cycles, the MAE, RMSE, and MAPE values are increased, but, overall, are in order of \(10^{-2}\), for MAE and \(10^{-1}\) for RMSE, while the maximum MAPE is 447 % on amplitude. (3) When increasing the number of cycles, the MAE, RMSE, and MAPE values are increased in amplitude and TOF. The trend in MAE, RMSE, and MAPE values of amplitude as well as TOF is, closely, following the increasing function with respect to increasing in future time step prediction. The apparent trend from Table 3 is that the performance of the SDL model prediction on reflected wave propagation simulation deteriorates, as the number of future time steps to be predicted increases. Even if we can observe that from Figures 6, 8, and 10, we can infer that the results obtained from the SDL model are in reasonably good agreement with the FE simulation until the t = 4.0 us frame, for all the domains. Still, there is some compounding errors that started accumulating time instances afterward. The generation of accurate waveform amplitude from back-wall reflection depends on the various parameters in the network architecture, such as the number of hidden layers, kernel size, input-output frames, etc. However, the best suitable learnable hyperparameters and network parameters need to be selected, which may require additional computational resources and time to train the model.