## 1 Introduction
The choice of FCDNN is for the reason that deep learning has a stronger model expression ability to produce a good fit for highly non-linear system behavior and the associated data of the complex interactions of the grinding system and, consequently, better prediction accuracy. Our further experience in practice validates and verifies its ability to capture the complexity of the grinding process accurately in the plant that the model was evaluated. Figure 1: A schematic of a closed-loop cement grinding control system. Adapted from [6]. This will be proved by the comparison of the results with other NN methods in the industry. In the following, we will review the existing literature on the cement grinding process prediction and optimization. Related Works Modeling and simulation of the cement grinding process are efficient tools for predicting and optimizing the process [7]. Modeling grinding circuits should consider several grinding operational variables such as the mill and separator details to name a few. In recent years, many strong grinding process simulation models have been developed to date. These models of industrial grinding circuits can be considered robust and highly accurate [8; 9]. The majority of the proposed models reported in the literature are a combination of physical laws of conservation of energy state and empirical correlations. Using empirical methods, an inferential model was necessary for many models as the real physics behind the phenomena is not very clear. This brings the necessity of constructing end-to-end model mapping of the inputs and the outputs of a grinding plant, possibly needing a grey box or black box method approach to solve the problem. One efficient solution to these problems is building data-driven dynamic models for integrated grinding circuits [2; 7]. These models are trained only on data collected from inlet and outlet streams of the grinding circuit and result in multiple-input-multiple-output (MIMO) system identification models. For advanced modeling of complex and non-linear dynamics process operations where an accurate mathematical model cannot be established, intelligence-based advanced methods have drawn the increasing attention of researchers [10]. Availability of a large amount of acquired data as an outcome of the deployment of advanced instruments, sensors, and novel networking technologies, which was not usually possible in the past, also justify this attention. Therefore, studying intelligence-based advanced methods by combining a large amount of production process data along with empirical knowledge of operators is an effective way to solve the advanced control problems in complex industrial applications where accurate mathematical models are difficult to establish [11]. The main characteristic of artificial intelligence (AI) technologies and machine learning (ML) techniques is their ability to emulate human reasoning through data and knowledge while avoiding human subjectivity and arbitrariness. Thus, with the growth in the development of AI and ML techniques in the recent past, the interest has shifted towards studying these techniques, and they have been widely used to deal with modeling and control problems of complicated industrial processes. Deep neural networks (DNNs) are examples of data-driven ML methods that have the characteristics of quick response and complex non-linear approximation to process with characteristics of nonlinearity, time-varying delay, and coupling. Therefore, DNNs are widely applied for non-linear problems in regressive prediction and show good performance in solving non-linear problems [3; 12; 13; 14]. For example, the recurrent neural networks (RNNs) (which is a type of DNN) methodologies are used to compete with prominent system identification tools, such as wavelet networks to model time series data [15; 16]. Long short-term memory (LSTM) networks are RNN-based methods capable of extracting features shared over an extended range of time and can be used with ML methods such as the regression method [17; 18].