# Rate of Penetration Prediction Method for Ultra-Deep Wells Based on LSTM-FNN
## 5 File Application  
In order to verify the migration effect of the intelligent ROP prediction model based on LSTM-FNN, we will take 80% of the data of well 1 as the training set and 20% as the test set, and use the optimal ROP prediction model to predict the ROP of well 2. In addition, prediction models of the ROP are established based on LSTM and FNN algorithms. The prediction accuracy of the model is shown in Table 4. The prediction results of the model are shown in Figures 7 and 8. Figure 7a-c are the partial prediction results of the FNN, LSTM and LSTM-FNN on test set 1, respectively. Figure 8a-c are the partial prediction results of the FNN, LSTM and LSTM-FNN on test set 2, respectively. As shown in Table 4, the relative error difference between the FNN and LSTM on the training set, test set 1 and test set 2 is small, about 1%. Although the LSTM ROP prediction model increases the time series information processing process compared with the FNN model, the accuracy of the model has not been greatly improved. As shown in Figure 9a, on the training set, the relative errors of the LSTM-FNN model are 4.17% and 5.07% lower than those of the LSTM and FNN models, respectively; on test set 1, the relative errors of the LSTM-FNN model are 4.92% and 4.91% lower than those of the LSTM and FNN models, respectively; on test set 2, the relative errors of the LSTM-FNN model are 7.33% and 8.07% lower than those of the LSTM and FNN models, respectively. After adding an FNN network to the output layer of the LSTM, the accuracy of the model is greatly improved. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Train Set Well 1 (80\%)**} & \multicolumn{2}{c}{**Test Set 1 Well 1 (20\%)**} & \multicolumn{2}{c}{**Test Set 2 Well 2 (100\%)**} \\ \cline{2-7}  & **MRE** & \(R^{2}\) & **MRE** & \(R^{2}\) & **MRE** & \(R^{2}\) \\ \hline FNN & 18.12 & 0.72 & 20.02 & 0.69 & 26.30 & 0.58 \\ LSTM & 17.23 & 0.83 & 20.03 & 0.71 & 25.56 & 0.65 \\ LSTM + FNN & 13.05 & 0.90 & 15.11 & 0.87 & 18.23 & 0.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Precision comparison of ROP prediction models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**LSTM**} & \multicolumn{2}{c}{**FNN**} & \multicolumn{2}{c}{**Model Parameters**} \\ \hline
**Step Length** & **Layers** & **Neural** & **Layer** & **Neural** & **Active Function** & **Learning Rate** \\ \hline
10 & 2 & 30 & 3 & 128 & ReLU & \(1\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: LSTM–FNN model parameter selection. Figure 8: ROP prediction results on test set 2: (**a**) ROP prediction results of FNN model; (**b**) ROP prediction results of LSTM model; (**c**) ROP prediction results of LSTM-FNN model. Figure 7: ROP prediction results on test set 1: (**a**) ROP prediction results of FNN model; (**b**) ROP prediction results of LSTM model; (**c**) ROP prediction results of LSTM-FNN model. It can be seen from Figure 9a that the MRE of the FNN model in the training set, test set 1 and test set 2 are 18.12%, 20.02% and 26.30%, respectively. The maximum MRE difference of the FNN model in the three data sets is 8.18%; the MRE of the LSTM model in the training set, test set 1 and test set 2 are 17.23%, 20.03% and 25.56%, respectively. The maximum MRE difference of the model in the three data sets is 8.33%; the MRE of the LSTM-FNN model in the training set, test set 1 and test set 2 are 13.05%, 15.11% and 18.23%, respectively. The maximum MRE difference of the model in the three data sets is 5.18%; the results show that LSTM-FNN not only has higher accuracy than the other two models on similar data sets and migrated data sets, but also has the lowest reduction in model accuracy. \(R^{2}\) is the fitting degree of the established model to the data, and the straight range is \([0,1]\). The closer \(R^{2}\) is to 1, the better the model is.