## 2 State of the Art  
Presently, the main modeling methods include mechanism analysis, data-driven identification, and the combination of the two. First, as the traditional modeling method, mechanism analysis can well interpret the internal operating principle of the system and fully reflect the physical characteristics of the plant [31; 32]. Unfortunately, coal-fired power plant is a huge and complex system with characteristics such as large inertia, large delay, non-linearity and strong coupling due to many equipment and mutual coupling of operation processes [33; 34; 35]. It is inevitable to propose numerous simplified assumptions, including simplified assumptions of equipment structure, working fluid status and lumped equipment parameters, which doubtlessly leads to poor predictive accuracy of the model [36]. In addition, due to slagging or oxidation, some parameters such as heat transfer coefficient and pipeline damping coefficient may change with equipment operation, deviating from the nominal values provided by the equipment manufacturers. This may affect the accuracy of the model more or less [37]. Second, the data-driven modeling method, also called the black box modeling method, learns the dynamic characteristic information of the plant through the input and output data [38]. Theoretically, if the number of neurons is sufficient, the neural network model can approximate the non-linear function with arbitrary accuracy [39]. In recent years, based on the data-driven method, the coal-fired boiler combustion model [40; 41], unburned carbon model of boiler [42] and output power prediction model [43; 44] have all achieved significant improvement. However, the accuracy of the black box model depends too much on the data quality. Insufficient data, excessive data noise and incomplete coverage of datasets may lead to poor generalization performance of the model [45]. Furthermore, the parameters are not interpretable and lack the mechanism formula to describe the relationship between variables [46]. Obviously, only using the mechanism modeling or data-driven method is hard to meet the requirements of digital twin for high-fidelity models. Compared with the above two methods, the hybrid modeling scheme can not only ensure the physical explanations, but also improve the predictive accuracy of the digital twin model. Presently, there are two main approaches. One is to establish mechanism model and identify parameters through input and output data [47; 48; 49]. This method can compensate most of the errors caused by the unascertained parameters, but it is powerless for the model errors introduced by mechanism simplification. The other is to compensate all errors of mechanism model by using learning algorithms such as neural network [37; 50; 51]. Although this method could improve the predictive accuracy of the digital twin hybrid model, it ignores the improvement of the predictive performance for the mechanism model. To deal with the above problems while ensuring the high fidelity of the digital twin model, this paper proposes a novel recurrent neural network-based hybrid modeling method which updates the mechanism parameters and data model parameters together. The main work of this paper includes the following four parts. First, the mechanism model of boiler system is established and then described through recurrent neural network (RNN) structure. In this way, the parameters in the mechanism model can be updated iteratively through the backpropagation algorithm, while the interpretability does not deteriorate. Second, the time-varying parameters in the mechanism model change with the change in input and state variables. By using neurons, the functional relationship between time-varying parameters and input variables is properly described to improve the predictive accuracy. Third, the long short-term memory (LSTM) neural network model is established to compensate the predictive residual of the mechanism model.