# AOSMA-MLP: A Novel Method for Hybrid Metaheuristics Artificial Neural Networks and a New Approach for Prediction of Geothermal Reservoir Temperature

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## Abstract

**:**

## Featured Application

**The proposed models can help uncover the usage areas of geothermal waters by determining the reservoir temperatures in advance. Thus, they can be used as a decision support system to make the most appropriate selection.**

## Abstract

^{2}value of 0.8514. The proposed AOSMA-MLP approach shows significant potential for yielding effective outcomes in various regression problems.

## 1. Introduction

## 2. Material and Methods

#### 2.1. Data Acquisition

^{−}is a major anion that enhances the salinity of geothermal fluids. The silica concentration, affected by temperature, is another crucial parameter. In a geothermal system, SiO

_{2}’s solubility decreases with falling temperature. Additionally, silica is vital for estimating reservoir temperatures in thermal springs, and its precipitation can influence the operational process. The dissolved ion content in geothermal fluids, indicative of the temperature and reservoir geology of an area, varies with temperature. Low-temperature fluids contain fewer dissolved solids than their high-temperature counterparts, making electrical conductivity (EC) an important measure for assessing dissolved particles in geothermal fluids [12].

#### 2.2. Artificial Neural Network

#### Multi-Layer Perceptron Neural Networks

_{ij}is the connection weight between the hidden neuron j and the input neuron i. b

_{j}is the bias value.

_{j}is the output value of neuron j, and f is the sigmoid function. Its calculation is shown in Equation (3).

_{j}is the final output of j.

#### 2.3. Whale Optimization Algorithm

#### 2.4. Ant Lion Algorithm

_{Antlion}is the matrix used to store each ant lion’s location.

_{OAL}is the matrix used to save each ant lion’s fitness.

#### 2.4.1. Random Walks of Ants

#### 2.4.2. Trapping in Antlion’s Pits

#### 2.4.3. Building Trap

#### 2.4.4. Sliding Ants towards Antlion

#### 2.4.5. Sliding Ants towards Antlion

#### 2.4.6. Elitism

#### 2.5. Slime Mould Algorithm and Adaptive Opposition Slime Mould Algorithm

**Case 1:**When ${\mathit{r}}_{\mathbf{1}}\ge \mathit{\delta}\mathrm{a}\mathrm{n}\mathrm{d}{\mathit{r}}_{\mathbf{2}}{\mathit{p}}_{\mathit{i}}$, the slime mould search trajectory is directed by the best local slime ${\mathit{X}}_{\mathit{L}\mathit{B}}$ and two randomly pooled slimes ${\mathit{X}}_{\mathit{A}}$ and ${\mathit{X}}_{\mathit{B}}$ with the velocity ${\mathit{V}}_{\mathit{b}}$. It balances exploration and exploitation. Case 1 indicates that ${\mathit{X}}_{\mathit{A}}$ and ${\mathit{X}}_{\mathit{B}}$ are arbitrarily combined slime mould; therefore, the solutions we acquire are not well explored and exploited [34]. This limitation may be solved by substituting ${\mathit{X}}_{\mathit{A}}$ with the best local ${\mathit{X}}_{\mathit{L}\mathit{B}}$. In this case, the equation can be updated, as shown in Equation (41).

**Case 2:**The slime mould trajectory is directed by its own location with a velocity ${\mathit{V}}_{\mathit{c}}$ when ${\mathit{r}}_{\mathbf{1}}\ge \mathit{\delta}\mathrm{a}\mathrm{n}\mathrm{d}{\mathit{r}}_{\mathbf{2}}\ge {\mathit{p}}_{\mathit{i}}$. This helps with exploitation. According to Case 2, the slime mould utilizes a neighboring location; thus, it may take a different route with a lower fitness value. An adaptive decision (AD) strategy might be a better option to overcome this limitation [34].

**Case 3:**When ${\mathit{r}}_{\mathbf{1}}<\mathit{\delta}$, in the search space, the slime mould re-initializes, assisting with exploration. Based on Case 3, the SMA provides a provision for devoted exploration; nevertheless, the exploration is limited since $\mathit{\delta}$ has a small value. We must add more exploration to SMA in order to assist it in circumventing this limitation and exceeding the local minima. To address the limitations of Cases 2 and 3, we employ an AD technique to determine if it is necessary to investigate further using OBL [34].

#### 2.5.1. Opposition-Based Learning

#### 2.5.2. Adaptive Decision Strategy

#### 2.6. Metaheuristic Optimization Algorithms for Learning Mlp

#### 2.7. Evaluation Metrics

^{2}, R, RMSE, and MAE, were used in this study. These metrics are widely used in the literature to compare the performances of the models proposed for predicting regression problems [40,49]. Equations of evaluation metrics are given in Equations (48)–(51).

#### 2.8. Normalization

## 3. Results

## 4. Discussion

^{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.

**R**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.^{2}Value:**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.

^{2}at 0.9959 [50]. In another study by Quan 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]. Perez-Zarate 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].

## 5. Conclusions

- 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.
- 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.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

EU | European Union |

RT | Reservoir temperature |

ANN | Artificial Neural Network |

FNNS | Feed-Forward Networks |

MLP | Multilayer Perceptron |

WOA-MLP | Whale Optimization |

ALO-MLP | Ant Lion Optimizer |

SMA-MLP | Slime Mould Algorithm |

AOSMA | Adaptive Opposition SMA |

EC | Electrical Conductivity |

Cl^{−} | Chloride ion |

K^{+} | Potassium ion |

B | Boron |

Na^{+} | Sodium ion |

SiO_{2} | Silicon dioxide |

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**Figure 4.**Experimental and predictive values of ANN, ALO-MLP, WOA-MLP, SMA-MLP, and AOSMA-MLP in hydrogeochemical and RT data.

Parameter | Unit | Value | |
---|---|---|---|

Input Data | pH | - | 2.4–9.7 |

EC | microS/cm | 203–10,434 | |

K^{+} | mg/L | 0.7–191 | |

Na^{+} | 2.6–2600 | ||

Boron | 0–38 | ||

SiO_{2} | 11–650 | ||

Cl^{−} | 2.8–2500 | ||

Output Data | RT | °C | 11–245 |

NA | NS | NTRS | NTS | HNO | Dim | W | B | NNS |
---|---|---|---|---|---|---|---|---|

7 | 161 | 128 | 33 | 15 | 136 | 120 | 16 | 7-15-1 |

Algorithm | Parameters | Values |
---|---|---|

WOA | $\overrightarrow{a}$ Shape of the logarithmic spiral ($b$) | Linearly decreased from 2 to 0 1 |

SMA | $\delta $ | 0.03 |

AOSMA | $\delta $ | 0.03 |

**Table 4.**Performance of ANN, ALO-MLP, WOA-MLP, SMA-MLP, and AOSMA-MLP on hydrogeochemical and RT data.

R^{2} | R | RMSE | MAE | |
---|---|---|---|---|

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 |

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**MDPI and ACS Style**

Gurgenc, E.; Altay, O.; Altay, E.V.
AOSMA-MLP: A Novel Method for Hybrid Metaheuristics Artificial Neural Networks and a New Approach for Prediction of Geothermal Reservoir Temperature. *Appl. Sci.* **2024**, *14*, 3534.
https://doi.org/10.3390/app14083534

**AMA Style**

Gurgenc E, Altay O, Altay EV.
AOSMA-MLP: A Novel Method for Hybrid Metaheuristics Artificial Neural Networks and a New Approach for Prediction of Geothermal Reservoir Temperature. *Applied Sciences*. 2024; 14(8):3534.
https://doi.org/10.3390/app14083534

**Chicago/Turabian Style**

Gurgenc, Ezgi, Osman Altay, and Elif Varol Altay.
2024. "AOSMA-MLP: A Novel Method for Hybrid Metaheuristics Artificial Neural Networks and a New Approach for Prediction of Geothermal Reservoir Temperature" *Applied Sciences* 14, no. 8: 3534.
https://doi.org/10.3390/app14083534