The DEA and anode recirculation modes are commonly used to improve the hydrogen utilization, especially for the automotive PEM fuel cell [12; 13; 14]. Nitrogen crossover and liquid water accumulation in the anode will occur that lead to the performance degradation. To improve the durability and operation stability of the PEM fuel cell, it is necessary to understand the degradation process under various working conditions. Compared to the experimental test, predicting the performance degradation process of the PEM fuel cell by modeling could reduce experimental time and expense. [PERSON] et al. [15] developed a three-dimensional single-channel computational fluid dynamics (CFD) model of the PEM fuel cell with the DEA, and processes of the performance decay under various operating conditions are predicted. [PERSON] and [PERSON] [16] developed a pseudo-three-dimensional transient model to analyze the dynamic and localized characteristics of the PEM fuel cell with the DEA. The numerical results of the performance decay were compared to the experiment results to validate the model. [PERSON] et al. [17] developed a control-oriented model of the PEM fuel cell with the DEA operation considering the internal transport mechanisms. The working processes under various purge intervals and purge durations were simulated and analyzed, and some critical indicators, such as pressure and nitrogen content, were monitored during the simulation. Furthermore, the calculated performance decay in the DEA operation, and performance recovery in the purge duration were validated by comparing to the experiment results. [PERSON] et al. [18] and [PERSON] et al. [19] developed a PEM fuel cell stack cold start model to investigate the cold start characteristics. The failure processes of cold start were well simulated and compared with experimental data. Three start modes, constant power, current and voltage, were analyzed, and the optimized cold start strategies were proposed based on the simulation results. [PERSON] et al. [20] used a bonobo optimizer (BO) algorithm to identify the unknown parameters of the PEM fuel cell model, and the simulation results could well match the experimental results. The BO algorithm also showed better performance than other optimization algorithms. [PERSON] et al. [21] developed a quasi-two-dimensional transient model of PEM fuel cells with anode recirculation. The transient characteristics of the cell with anode recirculation was investigated, including the performance improvement in the initial period due to self-humification and performance decay due to nitrogen crossover. Besides physical models, many studies developed data-driven models to predict the transient behaviors of PEM fuel cells [22; 23; 24; 25]. The data-driven model constructs the input-output relationship from the experimental dataset, and does not require much prior knowledge. Furthermore, after the model is well-trained, conducting the data-driven model does not require complex calculation, and the computational efficiency is generally much higher than that of the physical model [26; 27]. [PERSON] et al. [28] proposed a fusion prognostic approach based on particle filter and long short-term memory (LSTM) network. This approach could effectively predict the remaining useful life and short-term degradation of fuel cells. [PERSON] et al. [29] reported an attention-based recurrent neural network (RNN) model that could accurately predict the output voltage degradation of PEM fuel cells based on original long-term dynamic loading cycle durability test data. The attention-based LSTM and attention-based gated recurrent unit (GRU) showed the higher prediction accuracy compared to LSTM and GRU. [PERSON] et al. [30] presented the results of a long-term durability test performed on an open-cathode fuel cell system operating during 5000 h under specific operating conditions. A degradation model based on echo state network (ESN) was then used to predict the performance evolution.