## 3 Artificial Intelligence Methods for GWL Modelling  
### Artificial Neural Networks  
ANNs are some of the most powerful machine learning algorithms based on the structure and function of the human brain's neural system. These networks consist of neurons and their connections [11]. Each neuron in this network acts as a processing unit, with the weights corresponding to its connections determining the importance and impact of the inputs on the outputs [10]. The structure of an ANN typically includes three layers [12]: (1) the input layer is responsible for receiving the input variables; (2) the hidden layers, situated between the input and output layers, are responsible for the main information processing; and (3) finally, the output layer produces the result. The working method of ANNs in the training process involves providing inputs to the network, which produces corresponding outputs. The generated error is then compared with the desired output, and the network's weights are automatically adjusted to minimise the error. This process is repeated until the weights reach an optimal value, allowing the network to predict more accurately [13]. Figure 3 illustrates the classical structure of an ANN. It also shows the connections between the neurons, including all connections between the neurons of the input layer and the hidden layer and between the neurons of the hidden layer and the output layer. These connections represent the weights optimised during network training to provide the best result. Figure 2: Graphical representation of the trend in the number of scientific articles published between 2001 and 2023 on using different AI-based methods in GWL modelling. ANNs = Artificial Neural Networks; ANFISs = Adaptive Neuro-Fuzzy Inference Systems; SVMs = Support Vector Machines; DL = Deep Learning; GP = Genetic Programming; Hybrid = Hybrid Algorithms. In groundwater studies, ANNs are powerful tools with many applications [15]. These include GWL prediction, identifying geologic patterns associated with groundwater, and improving the performance of existing groundwater potential mapping. ANNs can improve cartographic models, increasing their predictive accuracy [16]. An analysis of 41 articles from 2001 to 2022 shows that ANNs are widely used worldwide, with India and Iran standing out as essential players (Figure 4). Ref. [17] conducted a study in the Yamuna-Hindon Inter basin, India, and found that the ANN Levenberg-Marquardt (LM) algorithm was slightly superior to that of Bayesian Regularisation (BR) and Back Propagation (BP) algorithms in GWL prediction accuracy. The input data included the maximum depth of the water table for agricultural  
Figure 4: Graphical representation of the trend in the number of scientific articles published between 2001 and 2022 on using ANN 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. Figure 3: Schematic representation of a classical ANN’s structure (more details in the text) (modified by [14]). purposes. Similarly, ref. [18] in Jaipur and Rajasthan, India, demonstrated that an ANN outperformed time series forecasting methods (e.g., ARIMA) in describing GWL and water quality parameters. The input data for this study included water levels. In [19], an investigation conducted in Tikri Kalan, West Delhi, India, a 3-15-1 ANN architecture was highly effective in predicting GWL fluctuations. Input data included rainfall, land use, and population. Likewise, [12] in Pakistan successfully used an ANN to predict daily GWL using input data such as rainfall, maximum and minimum temperatures, solar radiation, humidity, wind speed, and terrain elevation. A study by [8] in the Nabhana watershed in Tunisia showed that monthly GWL was influenced by rainfall, evaporation, and previous values. The input data included rainfall, previous groundwater levels, and evaporation. Ref. [11] Aquifer, South Khorasan, Iran, demonstrated that a Bayesian Network (BN) performed better than an ANN.