## 5 Conclusions  
In this study, the adaptive opposition-based slime mould algorithm (AOSMA) was innovatively applied during the training phase of the multilayer perceptron (MLP) for the first time. This novel approach was specifically tailored for predicting reservoir temperatures (RTs) and was benchmarked against a conventional first-order optimization technique, one-stage secant backpropagation, and three distinct stochastic metaheuristic optimization methods. The metaheuristic techniques compared included the whale optimization algorithm (WOA), ant lion optimizer (ALO), and slime mould algorithm (SMA), all of which are extensively recognized in the literature. Key findings from this comparative analysis are as follows:  
* The AOSMA-MLP demonstrated superior performance relative to the other metaheuristic optimization algorithms tested. By leveraging AOSMA for ANN training with hydrogeochemical and RT data derived from geothermal sources, it effectively addressed common limitations of alternative methods, such as susceptibility to local minima and constraints on global exploration capabilities.  
Figure 5: Scatterplots of the ANN, ALO-MLP, WOA-MLP, SMA-MLP, and AOSMA-MLP.  
* Across the board, AOSMA-MLP showcased a distinct advantage over competing methods across the four different evaluation metrics employed in this study. This underscores its efficacy and robustness in predicting RTs.
* In terms of accuracy of fit to the data, the AOSMA-MLP algorithm performed better than the ANN, WOA-MLP, ALO-MLP, and SMA-MLP approaches by 18.76%, 9.65%, 5.16%, and 7.03%, respectively.
* The promising outcomes achieved with AOSMA-MLP indicate its potential applicability across a broad spectrum of regression problems, extending beyond the scope of this study.
* 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.
* The application of the AOSMA-MLP model for predicting RTs in geothermal resources is projected to significantly aid engineers and project planners in identifying optimal drilling locations. Given the typically time-intensive, expensive, and complex nature of such determinations, this model can substantially reduce project costs and enhance flexibility within the investment and design phases of geothermal energy projects.
* Overall, the introduction and application of AOSMA-MLP represent a significant advancement in geothermal energy research, offering practical benefits for the planning and execution of geothermal projects.  
Conceptualization, E.G. and O.A.; methodology, E.G. and O.A.; software, O.A. and E.V.A.; validation, O.A. and E.V.A.; formal analysis, E.G. and O.A.; investigation, E.G. and O.A.; resources, E.G., O.A. and E.V.A.; data curation, E.G., O.A. and E.V.A.; writing--original draft preparation, E.G., O.A. and E.V.A.; writing--review and editing, E.G., O.A. and E.V.A.; visualization, E.G., O.A. and E.V.A.; supervision, E.G., O.A. and E.V.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data available on request from the authors.  
The authors declare no conflicts of interest.