## 4 Discussion  
To assess the effectiveness of the models proposed in this study, four widely recognized evaluation metrics were employed: R-squared (R\({}^{2}\)), correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE). The comparative results of the four models are systematically presented in Table 4, with the most favorable outcomes highlighted for clarity. A detailed analysis revealed the following insights based on the evaluation metrics:  
* **R\({}^{2}\) Value:** The AOSMA-MLP algorithm outperformed the ANN, WOA-MLP, ALO-MLP, and SMA-MLP methods by 18.76%, 9.65%, 5.16%, and 7.03%, respectively, indicating a more accurate fit to the data. * **R Value:** In terms of correlation, the AOSMA-MLP method exhibited superior performance by 6.11%, 2.94%, 2.03%, and 2.89% compared to the ANN, WOA-MLP, ALO-MLP, and SMA-MLP algorithms, respectively, suggesting stronger linear relationships between predicted and observed values. * **RMSE Value:** The AOSMA-MLP model demonstrated a significant reduction in prediction error, showing improvements of 27.56%, 18.46%, 11.65%, and 14.75% over the ANN, WOA-MLP, ALO-MLP, and SMA-MLP algorithms, respectively. * **MAE:** In terms of absolute errors, the AOSMA-MLP approach was found to be more precise, reducing errors by 26.74%, 15.08%, 16.44%, and 19.99% compared to the ANN, WOA-MLP, ALO-MLP, and SMA-MLP algorithms, respectively. Upon a comprehensive review of Table 4, the AOSMA-MLP model surpasses its counterparts across all evaluated metrics, establishing its superiority and effectiveness in predicting the reservoir temperatures (RTs) of geothermal resources. This comparative analysis underscores the potential of the AOSMA-MLP approach as a more accurate and reliable method for RT prediction in geothermal studies. In the study conducted by [PERSON], the RT value was predicted using linear regression, a linear support vector machine, and a deep neural network (DNN). A total of 83 different datasets were used in the study, and the best result was obtained in DNN. DNN achieved an MAE value of 6.45 and an RMSE value of 8.29 [12]. In the study conducted by [PERSON] et al., the RT value was estimated using natural gradient boosting (NGB), extreme learning machine, group method \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **R\({}^{2}\)** & **R** & **RMSE** & **MAE** \\ \hline ANN & 0.7169 & 0.8701 & 36.94 & 29.28 \\ WOA-MLP & 0.7765 & 0.8969 & 32.82 & 25.26 \\ ALO-MLP & 0.8096 & 0.9049 & 30.29 & 25.67 \\ SMA-MLP & 0.7955 & 0.8974 & 31.39 & 26.81 \\ AOSMA-MLP & 0.8514 & 0.9233 & 26.76 & 21.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of ANN, ALO-MLP, WOA-MLP, SMA-MLP, and AOSMA-MLP on hydrogeochemical and RT data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameters** & **Values** \\ \hline \(\overset{\rightarrow}{a}\) & Linearly decreased from 2 to 0 \\  & Shape of the logarithmic spiral (\(b\)) & 1 \\ \hline SMA & \(\delta\) & 0.03 \\ \hline AOSMA & \(\delta\) & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters of the metaheuristic optimization methods. of data handling, generalized regression neural network, and back propagation neural network methods. A total of 83 different datasets were used in the study, and the best result was obtained with the NGB method. The NGB MAE was calculated at 3.97, RMSE at 4.59, and R\({}^{2}\) at 0.9959 [50]. In another study by [PERSON] et al., the RT value was estimated using ANN, support vector regression genetic algorithm SVR, and improved support vector machine (M-GASVR) methods. The M-GASVR method yielded the best results in the study. The M-GASVR was calculated as MAE 0.45, RMSE 0.556, and R\({}^{2}\) 0.903 [51]. [PERSON] and colleagues conducted a study using different ANN models to predict the RT value. In the study, the ANN model that gave the best results was calculated as MAE 18.32, RMSE 26.4971, and R 0.7165 [24]. Figure 4 compares predicted and actual reservoir temperatures (RTs) using four distinct models.