## 4 Groundwater Level Prediction Techniques
### Deep Learning  
Despite the significant performances of ANN and ANFIS in accurately predicting the GWL, these methods were confined by the vanishing and exploding gradient problem, thus hindering the capability of the machine learning models to make predictions for long-time series. A recurrent neural network (RNN) is a type of neural network that was introduced to solve the long-term dependency problem when dealing with large-scale data in the temporal domain. However, regular RNN cannot remember temporal information for long sequences, i.e., in the machine translation tasks, etc., and require large computational resources. To overcome the limitations of regular RNN, the long short-term memory (LSTM) model was proposed to keep the information for an arbitrary length. LSTM is mainly developed for continuous data--time-series data. Recently, it has been employed in various water level assessment studies.  
[PERSON] et al. [6] proposed the LSTM model to simulate the fluctuations in water table levels using monthly water diversion, precipitation, evaporation, temperature, and previous water table level data spanning 14 years (2000-2013). The results achieved were dramatically high (\(R^{2}\) score, 0.789) when compared with the \(R^{2}\) scores (0.004-0.495) of the traditional feed-forward neural network (FFNN or regular ANN). To select relevant predictors, the authors used a statistical technique that contributed to the model's ability to generalize from the unseen data. The study was performed in five sub-areas of Hetao, China. GWL fluctuations data are prone to the existence of missing values because of several factors, i.e., human negligence, failure of recording equipment, etc. Gaps in data can make it difficult to grasp the hidden trends and seasonality. Therefore, this has led the missing values being reconstructed to fully interpret the data and make accurate predictions so that strategists can make plans for water resource management in the long run. [PERSON] et al. [72] evaluated the ability of an LSTM model against a traditional gap-filling algorithm, ARIMA, to fill missing temporal observations for a 10-year-long dataset with dynamic gaps. The model was designed to reconstruct specification measurements (groundwater and river water interactions). The results revealed that LSTM is better at filling high dynamic gaps (daily, weekly, and sub-daily), while ARIMA excelled in reconstructing trends and seasonality-based gaps. In addition, the authors reported that LSTM can fill gaps for up to 2 days when spatial data from neighboring stations are used to make predictions. Table 3 presents detail research categorized by different algorithms: deep learning, GP, MODFLOW, ANFIS, and ANN.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**References** & **Deep Learning** & **GP** & **MODFLOW** & **ANFIS** & **ANN** \\ \hline [PERSON] and [PERSON] [49] & & ✓ & & \\ [PERSON] et al. [4] & & & & ✓ \\ [PERSON] et al. [56] & & & & ✓ \\ [PERSON] et al. [5] & & & ✓ & ✓ \\ [PERSON] et al. [57] & & & & ✓ \\ [PERSON] et al. [62] & & & ✓ & ✓ \\ [PERSON] et al. [55] & & & ✓ & ✓ \\ [PERSON] et al. [64] & & & ✓ & ✓ \\ [PERSON] et al. [65] & & & ✓ & ✓ \\ [PERSON] et al. [69] & & ✓ & & \\ [PERSON] et al. [71] & & ✓ & & \\ [PERSON] et al. [6] & ✓ & & & ✓ \\ [PERSON] et al. [72] & ✓ & & & \\ [PERSON] et al. [73] & ✓ & & & \\ [PERSON] et al. [74] & ✓ & & & \\ [PERSON] et al. [75] & ✓ & & & \\ [PERSON] et al. [76] & & & & ✓ \\ [PERSON] et al. [77] & & & ✓ & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Research categorized by different algorithms: deep learning, GP, MODFLOW, ANFIS, ANN.