## 3 Artificial Intelligence Methods for GWL Modelling
### Genetic Programming  
GP is an AI-based method that uses algorithms inspired by natural selection to solve problems [4; 68]. GP is a subset of Genetic Algorithms and is often used to generate com  
Figure 10: Graphical representation of the trend in the number of scientific articles published between 2018 and 2023 on using DL 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. puter programmes, especially in domains where traditional algorithms may not perform well [2; 69]. In GP, codes are generated in a structured manner [70]. These structures are called \"species\" or \"individuals\" that genetic algorithms improve. Typically, a programme in GP is represented as a structured tree consisting of operators, operands, and variables [71]. Each node in this tree can represent an operator or an operand [72]. GP is applied in groundwater studies to model hydrological processes, optimise pumping strategies, predict GWL, identify influential factors, and design monitoring networks [68]. The structure of GP typically involves a tree-based framework, where various parameters, operators, and functions are arranged within nodes connected by branches. Each node in the tree comprises two distinct sets, i.e., a function set and a terminal set [2]:  
* Function set--nodes within the function set encapsulate mathematical functions like square, sine, and tangent; arithmetic operators such as addition, subtraction, and division; Boolean operators like AND and OR; and additional user-defined expressions; these nodes usually have child arguments. * Terminal set--nodes belonging to the terminal set consist of numerical constants and variables, representing inputs or random variables within the problem domain. Figure 11 shows an example of a GP model consisting of two tree-branch structures [2]. The left tree structure is \((7-X1)\times(X2+5)\), where X1 and X2 symbolise random variables. The right tree structure can be constructed as sqrt(Y1) + \((X1/8)\), where Y1 denotes another random variable. The GP's tree-based configuration essentially entails nodes embodying functions and terminals, structured hierarchically to formulate mathematical expressions or programmes to address specific problem-solving objectives. This study analyses 9 articles published between 2011 and 2023, providing an assessment of each article followed by a general conclusion drawn from them (Figure 12). Based on the research conducted by [4], Gene Expression Programming (GEP), particularly its three-gene structure, proves highly effective for GWL modelling. By leveraging time series data, this method captured the temporal variations and complexities inherent in the groundwater data of Urmie Lake, Iran. This study underscores the potential of GEP for providing accurate and reliable GWL predictions, which is essential for effective water resource management in the region. According to the investigations by [2], GP offers precise GWL predictions, with a notable emphasis on the strategic placement of weather stations. The study reveals that accurate weather station locations significantly enhance the  
Figure 11: Schematic representation of a GP classical structure (more details in the text). model's predictive capability. Ref. [70] research highlights that Gaussian Process Regression (GPR) surpasses GP in predicting groundwater salinity. The comparison demonstrates that GPR offers better precision and reliability in handling the complex relationships between pumping activities and salinity concentrations. In 2017, [73] introduced novel formulations integrating uncertainty into simulation and optimisation processes, showcasing improved accuracy and reduced computational time. Their method utilises GP combined with Continuous Ant Colony Optimisation and Monte Carlo simulation to handle various hydrological parameters. According to the research by [71], incorporating uncertainty quantification into GP-based methods is essential for refining GWL predictions.