## 3 Artificial Intelligence Methods for GWL Modelling
### Support Vector Machines  
SVMs, which also belong to the family of machine learning tools, have shown remarkable success in various hydrogeological applications, including GWL modelling [44; 45; 46]. Figure 6: Graphical representation of the trend in the number of scientific articles published between 2009 and 2023 on using ANFIS in groundwater studies. The size of the dots indicates the number of articles related to each country. The larger the number of articles, the bigger the dot. SVMs create an optimal hyperplane that classifies data points into different classes or predicts GWL, maximising the distance between classes to improve robustness and generalisation [47; 48]. SVMs are characterised by processing high-dimensional data and capturing complex patterns within the dataset, considering multiple influencing factors simultaneously and providing a holistic perspective on groundwater dynamics [49]. Their adaptability to various kernel functions, such as the RBF and polynomial kernels, further enhances their ability to model complex relationships within hydrogeological systems [50; 51; 52]. SVMs have been used to address prediction accuracy and uncertainty challenges, demonstrating robust performance compared to conventional methods and optimising water resource management and environmental planning [53; 54]. With the advances in machine learning, SVMs remain a valuable tool for predicting GWL and improving our understanding of subsurface hydrological processes [48]. In summary, the classical structure of an SVM is as follows [49; 50] (Figure 7):  
* Learning phase--the SVM algorithm seeks to find the optimal hyperplane separator between different classes in the training dataset;
* Choosing the SVM type--select the type of SVM among linear and nonlinear models and specify the kernel function to transform data into a higher-dimensional space if necessary;
* Determining hyperparameters--these are essential parameters such as kernel function and objective function like \(C\) for controlling the error rate and the number of misclassifications;
* Training--involves finding the SVM model using the training dataset and determining the optimal parameters;
* Evaluation--involves applying the model to test data to assess its performance and measuring evaluation metrics such as accuracy and confusion matrix;
* Tuning--after evaluating the model, we may need to re-adjust parameters or change the type of kernel function to improve model performance;
* Utilisation--the trained model is used to predict the class label of new data;
* Maintenance and update--if the model needs updating (e.g., with new data), it may need to be retrained or updated. This study analyses 14 articles published between 2011 and 2023, providing an assessment of each article followed by a general conclusion drawn from them (Figure 8). Figure 7: Schematic representation of a classical SVM structure (more details in the text). In the studies conducted by [3], a combined Wavelet Transform (WT) LSSVM was employed to predict GWL in the Saveh region, Iran. This combination performed better than independent methods using precipitation, evaporation, temperature, and GWL as input data. For instance, on specific days with high precipitation and low temperature, the WT-LSSVM could predict GWL with higher accuracy. Ref. [7] investigated the performance of an SVM for predicting GWL in the Azerbaijan region, Iran. The results indicate that the SVM outperformed other ANNs. For example, during the summer season, with increasing temperatures, the SVM can predict GWL variations with higher accuracy. A paper published by [55] examined the performance of the SVM-ALO (ant lion optimiser) in estimating monthly water levels in the Purbamediinpur region, India. The results show that this method performed very well. For instance, with seasonal variations in precipitation and temperature, the SVM-ALO could predict GWL changes with higher accuracy. Ref. [45] studied the GTB method's performance in predicting GWL one month ahead in the Karnataka region, India.