## 4 Results and Discussion
### Performance Evaluation of the LSTM Model  
This case study examined the robustness of the LSTM model in the synthetic Vp generation with sensitivity analysis on two parameters: the combination of input logging variables and the number of hidden neurons in the model. The model performance was \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Neural Network Algorithm & LSTM \\ Number of Layers (Input, Hidden, Output) & (\(1,1,1\)) \\ Optimizer & Adam \\ Dropout Rate & 0.25 \\ Ratio of Data (Training, Validation, Test) & (70\%, 15\%, 15\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the LSTM model used to generate synthetic Vp. Figure 5: Flowchart for generating synthetic Vp. assessed in terms of the \(R^{2}\) and RMSE using Equations (9) and (10), respectively. For finding the optimal input combination among the input set (GR, RHOB, RT, PEF, and TNPH), up to five inputs were imported into the LSTM model. Because the number of hidden neurons affects the model performance [55], we set up the number of hidden neurons in powers of two (i.e., 2 m) and increased the exponent m from zero to seven for each learning-based model. Considering eight scenarios for the number of hidden neurons for each input combination, 248 (= 8 \(\times\) 31) experiments were conducted in total, where 31 = 5C\({}_{1}\) experiments from one input (Table A1) + 5C\({}_{2}\) experiments from two inputs (Table A2) + 5C\({}_{3}\) experiments from three inputs (Table A3) + 5C\({}_{4}\) experiments from four inputs (Table A4) + 5C\({}_{5}\) experiment from five inputs (Table A5). Refer to Appendix A for the performance evaluation results of all experiments. Figure 6 illustrates radar charts to compare the \(R^{2}\) values obtained using the LSTM model for the 248 experiments: training results (Figure 6a), validation results (Figure 6b), and test results (Figure 6c). Nine wellbores, UBGH2-1_1, UBGH2-1_2, UBGH2-2_1, UBGH2-3, UBGH2-4, UBGH2-5, UBGH2-7, UBGH2-8, and UBGH2-9, were used for training, UBGH2-10 and UBGH2-11 for validation, and UBGH2-2_2 and UBGH2-6 for testing, UBGH2-6 and UBGH2-2_2 were selected as test data to judge whether the LSTM model could generate synthetic Vp with reliability. We intended to include UBGH2-6 in the LSTM test dataset because it was the only production test well in the UBGH field [32]. Similar to UBGH2-6, UBGH2-2-2 was a wellbore drilled at high-quality gas-hydrate-bearing sediments [44]. For the experiments with a single input variable (Table A1), the average \(R^{2}\) for the training, validation, and test data were 0.720, 0.446, and 0.514, respectively. In most experiments, the training \(R^{2}\) values were above 0.70 when using more than two neurons in the hidden layer. However, the average \(R^{2}\) values for validation and test data were approximately 0.50, which is less satisfactory than the training results. The model obtained high performance in the descending order of inputting PEF, TNPH, RHOB, GR, and RT, with average \(R^{2}\) values of 0.593, 0.581, 0.573, 0.571, and 0.553, respectively. These values improved by more than the Pearson correlation coefficients based on linearity in Table 1. The sensitivity analysis results for a single input variable indicate that LSTM is more efficient in capturing a nonlinear relationship between input and output. The combination with four input variables had the highest average \(R^{2}\) value among the five input combinations. As illustrated in Table A4, the highest performance was attained from the experiment inputting GR, RHOB, TNPH, and PEF with 64 hidden neurons: \(R^{2}\) values of 0.930, 0.711, and 0.8481 for the training, validation, and test datasets, respectively. Furthermore, it is essential to balance accuracy and computational cost. The LSTM model with 64 hidden neurons was superior to the model with 128, while the latter required a more complex neural network structure. The numbers of trainable LSTM parameters were 17,729 and 67,713, with 64 and 128 hidden neurons, respectively.