## 4 Results and Discussion
### SDL Model Implementation on Datasets Type-2: Reflection Wave Propagation Simulation  
A similar approach is followed from Section 4.1 to train the SDL model using the type-2 datasets of reflection wave propagation simulation (from Section 2.3). The SDL architecture consists of six layers of an encoder structure and six layers of a decoder structure; these structures are stacked together. Each encoder or decoder structure contains 256 hidden dimensions, and during convolutional operation, a \(5\times 5\) kernel size and the same padding are used. The average loss value over the number of epochs is shown in Figure 2(b). The average training loss is determined to be \(1.0\times 10^{-5}\), the testing loss is \(4.0\times 10^{-5}\), and the loss value becomes stabilized with an increase in the number of epochs. 2.1 Generalization to Different Geometrical Boundary Modelling: Reflected Wave Propagation from Boundaries  
To generalize the SDL model, we have modeled the ultrasonic wave propagation in four different geometrical domains: curved, T-shaped, and triangular. The SDL model predicted simulation is compared with the FE. Figure 5(a)-c shows the reflected ultrasonic wave propagation simulation for curved, T-shaped, and triangular domains, respectively. In each figure, the top row simulations are from the FE, and the bottom row shows the predicted simulation from the SDL model. During the training process, the proposed SDL model is trained with straight edge boundaries, but it could generate the simulation for curved boundaries (Figure 5(a)) and diagonal boundaries (Figure 5(c)). The SDL model has learned the wave interactions at the domain sharp edge and could generate the reflection wave propagation from the sharp edges (Figure 5(b)). So, the SDL model accurately predicts reflection wave propagation from the side and back walls as well as matches with the FE. Figure 6: _Cont._Quantitatively exploring the SDL model prediction on reflected wave propagation, we have extracted the displacement values along the line at x = 20 mm and y = 0 to 40 mm, from all the geometrical domain frames. Figure 7 shows the wavefront line scans between the SDL and FE model, for all the geometrical boundaries datasets. The SDL model-based line scans follow a similar trend to FE simulation-based line scans. To find out the amplitude and TOF difference between the two methods, we have employed MAE, RMSE, and MAPE, to calculate the error on each frame. A similar approach is adopted from Section 4.2. The comparison summary is shown in Table 2 for each frame for each domain. The maximum MAE is in order of \(10^{-2}\), the maximum RMSE is in order of \(10^{-1}\), and MAPE is 78.7% on amplitude error, over all the time frames. The maximum MAE is 1.86, the maximum RMSE is 2.56, and MAPE is 5.37% on an error in TOF, between all the geometrical domains. The SDL model could simulate curved domains (Figure 5(a)), sharp corner reflection (Figure 5(b)), and diagonal boundaries (Figure 5(c)), even though we have not used these geometries based datasets while the training process. The SDL model-generated simulations are reasonably in good agreement with FE simulation. Figure 6: Reflected wave propagation with different geometrical boundaries: FE and SDL models are used to simulate reflected wave propagation in different geometrical boundaries. The simulations generated using FE and SDL are compared to each other at identical time steps for different time instances. These simulations are modeled with an incident wave of 5 MHz frequency with two cycles, using a single-point excitation source on the top edge. (**a**) Represents the FE/SDL simulation for the curved domain, (**b**) illustrates the FE/SDL wave propagation simulation for the T-shaped domain, and (**c**) shows the wave propagation simulation for the triangular domain. For the illustration, a yellow dashed vertical line is created, manually, in all the frames, to extract the displacement values.