## 4 Results and Discussion
### Impacts of ML and MM Approaches on GWL Changes  
When ML is compared to mathematical model techniques, the application of machine learning approaches for groundwater level changes has increased throughout the years. The application of single machine learning algorithms and the presentation of novel methods are the most significant contributions of ML and MM approaches in predicting groundwater level variations. Due to the difficulty of computational complexity in machine learning algorithms [94], research towards lowering computational times is required and significant. Although computational complexity can impair application performance, several studies have found that performance times are reduced. As utilized in studies by [PERSON] et al. [2] and [PERSON] et al. [95], the employment of some ensembles of machine learning and metaheuristic algorithms helps to minimize computational time and enhances the prediction of groundwater level changes.  
Furthermore, model performance and computing efficiency are critical, and mathematical models are not excluded. Our primary research revealed that MM techniques have not been applied in a long time, resulting in a gap. However, it is important to recognize their significance in anticipating groundwater level variations. Researchers said in a study by [PERSON] et al. [96] that \"there is no viable mathematical approach and theory to be utilized for modeling and predicting the fluctuation in the permafrost groundwater\", but they did not rule out the use of mathematical models in predicting groundwater level variations.  
This research has added to our understanding of the machine learning and mathematical models commonly used in predicting groundwater level changes, revealing that machine learning models are used more frequently than mathematical models, with the former providing more effective ways to predict groundwater level changes. Also, SVM [18], RF [38], ensembles of ML [36], and some statistical techniques [13] can increase accuracies, computational efficiency, and performance in groundwater level change prediction. [PERSON] et al. [11] also proved that using imagery to predict groundwater level fluctuations improves prediction performance.  
Currently, the application of machine learning ensembles has been shown to produce higher accuracies in predicting groundwater level fluctuations. For example, [PERSON] et al. [36] showed that ensembles improve prediction accuracy, achieving an accuracy of 89.3 percent, which is the current attained accuracy for ensembles based on our core articles (117 articles). The improvement of planning and management of water resources depends on the development of an accurate soft computing method for groundwater level (GWL) forecasting [97], and this study has brought great news to the literature by revealing that random forest (RF) [10], support vector machine (SVM) [36], and artificial neural network (ANN) [9] methodologies are widely used machine learning algorithms for modeling groundwater level changes. Additionally, the most often employed GWL predictor factors were identified by this study (Table 4). Our research has shown that machine learning, including its  
\begin{table}
\begin{tabular}{c c} \hline \hline
**MM Approaches** & **Performance Metrics** \\ \hline LT & RMSE, EF \\ LHFM & CRM, CD \\ Boussinesq equation & CD, CRM, EF \\ Bayesian modeling & Posterior, predictive checks, AIC, RMSE \\ Rheological model & EF, RMSE \\ Glover–Dumm model & CRM, R, R\({}^{2}\) \\ Proposed Models & RMSE, MAE, AIC, etc. \\ \hline \hline \end{tabular}
\end{table}
Table 7: MM approaches and performance metrics.  
hybrid [7] and ensemble [8] models, operates flawlessly when employing satellite images by increasing computing complexity and processing time.