## 2 Research Methodology
### Prediction Models  
#### 2.2.1 Artificial Neural Network (ANN)  
Artificial neural network (ANN), which was introduced by [PERSON] and [PERSON] [82], is an intelligence mathematical technique of high popularity. This technique is capable of mimicking the complicated nonlinear relationships between input and output parameters on the basis of various environments. It is actually a simulation of the human brain neural mechanisms. ANN is an efficient parallel processing architecture containing at least a single hidden layer as well as input and output variables. It effectively handles fuzzy information where the functional relationships are not clear [80; 83; 84]. In ANN, through training, preceding samples, and experiences, the models can be created. It can be said that based on various training data, those patterns that are utilized to collect the neurons and outputs are mutative. Neurons construct the foundation of an ANN; they form the network organization. The neurons construct the layer(s) and the contextual layers have connection with each other through interconnection weights. ANN has been presented in lots of patterns among which the feed-forward-back-propagation (BP) is of a high practicality and has been used effectively in a number of studies [85; 86; 87]. Various inputs exist in each neuron. In the course of a training process, an output is produced by these inputs. Within ANN, neurons are in a full connection with each other, and the output of each unit element will be used as a new input for the following unit element. The layers in this system are composed of multiple neurons; the information is transmitted from the first layer to the next one in the course of training process and then the network response is produced by the last layer. The intermediate layers (also called hidden layers) are located between the input and output layers [88]. Numerous algorithms have been proposed in the literature on the basis of ANN; among them, BP is recognized of the highest popularity when there is a need for the interpretation of the network modification behavior [89]. In general, the error correction learning law is implemented in BP in which the error propagation actually adjusts the connection weights in a way to decrease as much as possible the sum of the mean squared error within the output layer. That is, the learning propagation comprises two phases: forward phase and back phase. In the former, a series of outputs is provided by the layer inputs transmission. In the latter, synaptic weights are obtained. To evaluate the efficiency of the above-mentioned model performance, two statistical indicators are taken into account, namely the coefficient of determination (R\({}^{2}\)) and the root mean square error (RMSE) [90; 91].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Abbreviation** & **Unit** & **Min** & **Max** & **Average** & **Std** \\ \hline Soil permeability coefficient & K & cm/s & \(1\times 10^{-10}\) & \(1\times 10^{-4}\) & \(1.59\times 10^{-5}\) & \(3.45\times 10^{-5}\) \\ Height water & HW & m & 10 & 48 & 29 & 10.89 \\ Freeboard & FB & m & 2 & 5 & 4 & 1.12 \\ Upstream slopes & \(\beta\) & degree & 15 & 30 & 23 & 5.59 \\ downstream slopes & \(\alpha\) & degree & 15 & 30 & 23 & 5.59 \\ Width crest & WC & m & 8 & 12 & 10 & 1.63 \\ Seppage rate & Q & m\({}^{3}\)/s & \(7.81\times 10^{-11}\) & \(1.48\times 10^{-3}\) & \(8.82\times 10^{-5}\) & \(2.22\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The statistical details of the dataset in this research.