## 4 Groundwater Level Prediction Techniques
### Machine Learning--Artificial Neural Networks (ANN)  
ANN is computational representation of a mathematical model inspired by the human brain's biological network. Simple elements called neurons, operating in parallel, constitute ANN [50]. ANNs are used to calculate unknown functions or to make future predictions of the given time series based on historical data. The most basic ANN is a three-layer structure, with input, hidden, and output layers [51]. The structural representation of classical FFNN into the network and the desired outcome is computed by the output layer. The hidden layer nodes which are situated between the input and output layers receive a set of scaled inputs and calculate an output after applying a certain learning (activation) function [52].  
A sample dataset Is used to train the ANN model. Training is a process of fine-tuning the network's adjustable parameters (known as weights and biases) to optimize the output of the algorithm. \"The Levenberg-Marquardt (LM) algorithm, the backpropagation (BP) algorithm, the Bayesian regularization (BR) algorithm, and the gradient descent with momentum and adaptive learning rate back-propagation (GDX) algorithm\" are some learning algorithms that have been employed to train models in the literature. Feed-forward neural networks (FFNNs), usually known as multilayer perceptrons (MLPs), are a popular and robust type of ANN that has been widely studied in hydrological studies [53]. Figure 4 shows the different kinds of data used for prediction the GWL.  
ANNs have been widely used in hydrology, hydraulics, rainfall-runoff estimation, groundwater level, and quality forecasting [54; 55; 56]. According to recent GWL modeling studies, it has been reported that ANN simulations have shown promising results compared to conceptual techniques. In one of the first studies, [PERSON]  
Figure 4: Different kinds of data used for prediction of GWL.  
simulate monthly groundwater (GWL) for an aquifer. Inputs included evapotranspiration, averaged temperature, precipitation, rainfall, and GWL at the previous lag of 13 piezometers and the primary objective was to anticipate GWL for a specific piezometer in northern France. The advantage of the multi-layer perceptron MLP was proven by simulation results. [PERSON] et al. [57] compared several types of FFNNs to simulate the monthly GWL in Andhra Pradesh urban aquifer, India. Results revealed the merit of an ANN trained with the LM algorithm as compared to BP and BR algorithms. Moreover, in the experiment, the best-performing network model parameters were used to predict the GWL in nearby wells.  
[PERSON] et al. [5] developed ANFIS and FFNN with an LM algorithm to estimate GWL for India's Maheshwaram watershed. Monthly groundwater (GWL) of 22 wells, rainfall, temperature, evaporation, and relative humidity are among the input variables. FNN outperformed ANFIS in terms of accuracy when results were compared. [PERSON] et al. [58] compared multiple FFNN networks and learning methods to simulate the daily groundwater (GWL) in a well. The study area is located in Montgomery County, Pennsylvania, USA. The best model was found to be FFNN trained using the LM learning algorithm with the humidity, precipitation, and temperature as inputs.