# Parallel-Structure Deep Learning for Prediction of Remaining Time of Process Instances
## 4 Experimentation and Results
### Results  
In this subsection, we will discuss the results of the experiments conducted. In Figure 6, we demonstrate the loss (MAE) trend of the training of the four models on one of the iterations of CV. We show only one of the five folds, because the pattern is like the other folds, which means that the training process for the five folds can be said to be consistent. MLP + EE and CNN + EE tended to be the same, MLP + EE more quickly experiencing overfitting conditions due to having less input (without chart images), so that we stopped the training process earlier than with CNN + EE or CNN + DAEE. CNN + DAEE experienced a relatively unstable training process at the beginning. The point where the last or best weights are \begin{table}
\begin{tabular}{c c} \hline \hline
**Component** & **Specification** \\ \hline CPU & Inter(R) Core (TM) i7-7700 HQ CPU @ 2.80 GHz 2.81 GHz \\ GPU & NVIDIA GeForce GTX 1050—4.0 GB Dedicated GPU Memory \\ Memory & 16 GB \\ Operating System & Windows 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental-environment specifications. Figure 6: Training and validation loss curves of four models. stored is when the validation test reaches the lowest point. Also, as shown in Figure 6, in the graph for DA-LSTM specifically, there is a spike that occurs before returning to stability. Such a spike is a common thing that can happen if we use a batch strategy in the training process. We also show, in Figures 6-11, prediction results for all five iterations of CV using the four models. Please note that the graph of the ground truth looks different in each of the four models because the scale is relative to the maximum value of predicted results by each model. We can see from the patterns that the four models provide reasonable predictions. MLP + EE, CNN + EE, and CNN + DAEE tend to have the same prediction results relative to DA-LSTM and to be more accurate, though, at some points, there can be vast differences between actual values and predicted values. For example, in Figure 7, our model considers some values as outliers, and because it optimizes MAE, the outlier is calculated as a minor penalty. To show the tangible difference of our proposed model in terms of accuracy, we provide a comparison of the errors in MAE and the training time required for each of the four models in Tables 8 and 9, respectively. We can see that CNN + DAEE outperforms the other three models for all iterations. MLP + EE is superior to both models in terms of training duration, far superior to DA-LSTM, but only slightly superior to CNN + EE and CNN + DAEE because it has the same model structure, except that MLP + EE does not receive chart images as its input and lacks the CNN component. The duration of performance training of CNN + DAEE is slightly superior to that of CNN + EE; this was caused by the length of the vector input generated using DAEE was less than that generated using Entity Embedding. Figure 8: Comparison of results of four models for 100 sample test sets in second iteration of CV. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Iteration**} & \multicolumn{4}{c}{**Training Duration (Minutes)**} \\ \cline{2-5}  & **DA-LSTM** & **MLP + EE** & **CNN + EE** & **CNN + DAEE** \\ \hline
1 st & 14:38 & 01:22 & 02:31 & 02:19 \\
2 nd & 15:16 & 01:16 & 02:35 & 02:03 \\
3 rd & 15:00 & 01:16 & 02:36 & 02:05 \\
4 th & 12:12 & 01:13 & 02:36 & 01:39 \\
5 th & 15:01 & 01:50 & 02:39 & 02:09 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Training duration in hours: minutes format. Figure 9: Comparison of results of four models for 100 sample test set in third iteration of CV. To show the tendency and ratio visually, we also show, in Figure 12's histograms, a performance comparison in terms of MAE and training duration. There it can be seen that MLP + EE, CNN + EE, and CNN + DAEE are far superior to DA-LSTM in terms of the time needed for training. In terms of accuracy, all four models show a consistent trend across all iterations, CNN + DAEE being the best model.