# A Review of the Artificial Neural Network Models for Water Quality Prediction
## 1 Introduction  
Water quality plays an important role in any aquatic system, e.g., it can influence the growth of aquatic organisms and reflect the degree of water pollution [1]. Water quality prediction is one of the purposes of model development and use [2], which aims to achieve appropriate management over a period of time [3]. Water quality prediction is to forecast the variation trend of water quality at a certain time in the future [4]. Accurate water quality prediction plays a crucial role in environmental monitoring, ecosystem sustainability, and human health. Moreover, predicting future changes in water quality is a prerequisite for early control of intelligence aquaculture in the future [5]. Therefore, water quality prediction has great practical significance [6]. At present, there are many traditional water quality prediction methods, such as multiple linear regression (MLR) [7], auto-regressive integrated moving average (ARIMA) [8], etc. MLR is not able to detect a nonlinear relationship between water quality parameters because of its linear inherence [9]. The main drawback of ARIMA is the pre-assumption of the linear model [10]. During the model identification phase, the time series data must be checked to see whether they are stationary or not, because it is critical in creating the ARIMA model. In fact, traditional methods are not able to capture the non-linear [11] and non-stationarity [12] of water quality well due to their complex and sophisticated nature. With the increase in data scale, traditional techniques cannot meet the demand of researchers. Owing to the improvement of computing power, artificial neural network (ANN) models, data-driven models, have been further developed. They can capture functional relationships among the water quality data from the examples [13]. When the underlying relationships of obtained data are difficult to describe, ANN models still work. Moreover, ANNs require fewer prior assumptions [14] and can achieve higher accuracy [15] compared with traditional approaches. In addition, ANNs are suitable for solving the non-linear and uncertain problems due to their similar characteristics with the brain nervous system [4], and have become a hotspot in water quality research [16]. ANNs are a family of models inspired by biological neural networks [17] which specifically refers to the human brain [18], a kind of central nervous system of animals. In general, ANN can be represented as a system of interconnected \"neurons\" [19] which form the basis of neural network operation. Weight parameters and activation functions are part of the neurons [20]. ANNs are generally divided into three layers of input, hidden and output. When neurons receive information from different inputs, they obtain nonlinearity through activation functions. ANN models depend heavily on the quantity of data [21]. Therefore, it is not recommended to use relatively small data sizes for predictors (inputs). This is because some useful information is lost in short-term data, which may lead to poor prediction results [3]. In addition, data dividing is a necessary step in the modeling process. Furthermore, choosing the training algorithm to calibrate the model parameters (e.g., connection weights) is a vital step so that the network can approximate complicated non-linear input-output relationship [10]. The Levenberg-Marquardt [22] algorithm and the back-propagation (BP) algorithm [23] are the most commonly used algorithms. ANN models architectures determine the number of connection weights and the way information flows through the network [20]. The most widely used architecture is Multilayer Perceptron (MLPs) with only three layers in many types of feedforward ANNs. Radial Basis Function neural networks (RBFNNs) [24], General regression neural networks (GRNNs) [25] and Extreme learning machines (ELMs) [5] are three typical feedforward ANNs. A Long Short-Term Memory (LSTM) neural network is an improvement of recurrent neural networks (RNNs), which aims to address the well-known vanishing gradient problem [26].