## 4 Results and Discussion
### Performance Evaluation of the LSTM Model
Based on these results on accuracy and computational cost, we decided to use the LSTM models with 64 hidden neurons. Moreover, the input set of GR, RHOB, TNPH, and PEF was selected as the optimal input combination for the model for subsequent analysis. An ANN model was built to compare its performance with that of the LSTM model to confirm the suitability of the LSTM model for sequential logging data analysis. Under the same data conditions and neural network configuration, we designed the structure of the ANN model similar to that of the LSTM model in terms of the numbers of trainable parameters: 17,813 for the ANN model and 17,729 for the LSTM model. Figure 7 illustrates the scatter plots between the reference and generated Vp data obtained using the two neural network models. This case corresponds to Fold 1 of the 10-fold cross-validation. \(R^{2}\) values for the training, validation, and test data obtained using the LSTM model were 0.931, 0.757, and 0.851, respectively. In contrast, the ANN model yielded unsatisfactory values of 0.415, 0.007, and 0.395. Furthermore, the RMSE decreased by more than 0.3 when applying the LSTM model compared with the ANN model. The ANN model failed in generating synthetic Vp. Figure 6: _Cont._  
Interestingly, the validation performance also deteriorated for the LSTM model when the reference Vp was larger than 6 because of incompatibility between the training and validation data ranges. Training and test data mostly ranged from -2 to 6 and validation data from -2 to 12. Furthermore, the training data were sparsely distributed when the reference Vp was larger than -6. These results imply the intrinsic limitation of the machine learning advantage in interpolation compared to extrapolation. The influence of the data range was investigated by re-comparing the performance of the two neural network models with different training and validation data (Figure 8); this case is Fold 3 of the 10-fold cross-validation. Wellbores UBGH2-10 and UBGH2-11 were included in the training data, and wellbores UBGH2-1_1 and UBGH2-1_2 were included in the validation data. Switching these data produced similar ranges for training and validation, improving the validation performance for both models while maintaining their training and test performance: The \(R^{2}\) of ANN increased from 0.007 to 0.119, and the \(R^{2}\) of LSTM increased from 0.757 to 0.920. This result highlights the importance to let each dataset (training, validation, and test) have a similar data distribution for making an accurate machine learning model. Nevertheless, the ANN's poor \(R^{2}\) values reveal a vulnerability in the sequential data analysis. Furthermore, despite the validation performance, the test performance of the LSTM model was satisfactory in each figure because the range of the test data was within the training data. Based on these results, we attest that the LSTM model outperforms the ANN model for sequential data analysis and reconfirm the significance of balancing the training and validation data ranges in deep learning. We also conducted a sensitivity analysis for the learning rate and batch size to create a cost-effective LSTM model. Determining the proper values for these hyperparameters is vital because a large learning rate might cause overshooting, while a small learning rate requires expensive computational costs [56]. Batch size also affects the model generality [57]. The effects of batch size and learning rate on \(R^{2}\) and computational time were analyzed  
Figure 6: Comparison of the \(R^{2}\) values for input combinations at various numbers of hidden neurons. for test data using the LSTM model depicted in Figure 7. The computational time was the arithmetic mean from four learning rate cases in each batch size. Figure 7: Scatter plots comparing the reference and predicted Vp data (scaled) for the training, validation, and test data for the ANN and LSTM (Fold 1).