## 4 Results and Discussion
### Comparisons of Different Deep Learning Models  
A detailed and comprehensive comparison of different methods was conducted using field shale gas production data. The outcomes indicated similar performances for both wells, thereby prompting the designation of well MIP-3H (referred to as \"well1\") as the illustrative case for the principal discourse. Well1 serves as an exemplar, demonstrating the approach's efficacy. In this context, 10% of the dataset (comprising the final 140 days) was allocated for testing the short-term production prediction, 20% (encompassing the last 280 days) for the medium-term prediction evaluation, and 30% (covering the last 420 days) for the long-term prediction assessment. Detailed production particulars for both wells, as well as the dataset divisions pertaining to the respective testing intervals, are outlined in Table 4.  
The fine-tuned GRU-MLP model was employed to predict daily gas production for well 1 (MIP-3H), leveraging both the daily gas production data and pertinent geological and engineering variables delineated in Table 2 for the predictive endeavor. Additionally, two other recurrent neural networks, specifically GRU and LSTM, were selected as benchmarks for comparison with the hybrid GRU-MLP model. To ensure parity in the comparison, the hyperparameters of two neural networks were set to align with the GRU component of the GRU-MLP model. Table 5, accompanied by Figure 8, presents the mean prediction errors of the three neural networks with regards to gas production. The observations derived from this analysis reveal that among the considered networks, the hybrid GRU-MLP network consistently showcases diminished prediction errors in comparison to both the LSTM and GRU networks. The observations underscore the hybrid GRU-MLP model's capacity to merge the inherent strengths of the GRU and MLP models, fostering heightened accuracy in forecasting daily gas production. Table 5 in conjunction with Figure 8 highlights the models exhibit better performances, particularly in the context of short-term predictions. This trend is in line with the common tendency in deep-learning-based models, where predictive accuracy often hinges on the volume of input samples. Figures 9-11 juxtapose the daily gas production forecasts engendered by the GRU and GRU-MLP models for well 1 (MIP-3H). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Well** & **Well Name** & **Start Date** & **End Date** & **Production Time (Days)** & **Short-Term Prediction (Days)** & **Medium-Term Prediction (Days)** & **Long-Term Prediction (Days)** \\ \hline Well1 & MIP-3H & 12/12/2015 & 7/8/2021 & 1931 & 194 & 387 & 580 \\ Well2 & MIP-5H & 12/11/2015 & 7/8/2021 & 1835 & 184 & 367 & 551 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Production data for two wells and dataset partitioning. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Neural Network** & **Hyperparameter** & **Value** \\ \hline \multirow{6}{*}{GRU} & No. of hidden layers & 3 \\  & No. of neurons in the hidden layers & [251; 192; 102] \\  & Dropout rate & 0.1 \\  & Batch size & 64 \\  & Epochs & 100 \\  & Loss function & MSE \\  & Optimizer & Adam \\ \hline \multirow{2}{*}{MLP} & No. of hidden layer & 1 \\  & No. of neurons in the hidden layer & 32 \\ \cline{1-1}  & Activation function & Relu \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fine-tuned hyperparameters for the GRU-MLP model. Figure 8: Evaluation metrics for diverse model performances. (**a**) RMSE values; (**b**) MAE values; (**c**) MAPE values. Figure 9: Comparisons of the final 194 days of production (short-term) for well 1: real data vs. GRU and GRU-MLP predictions.