## 1 Introduction
Although multi-dimensional models can provide high-resolution temperature distributions and accurately reflect the performance, it is impractical to use multi-dimensional models in experiments to improve the thermal management control accuracy and response speed due to high time and computational costs. Therefore, it is necessary to develop high-efficiency mechanistic models that can be applied in real-time control. [PERSON] et al. [17] developed a zero-dimensional (0D) water and thermal management model. They tested different coolant types and concluded that changing coolant type and temperature can effectively improve the performance of thermal management systems. [PERSON] et al. [18] established an eighth-order non-linear thermal model of an automotive fuel cell system and constructed a reduced-order model for comparison. The results indicated that the reduced-order model could accurately represent the performance of the non-linear model. [PERSON] et al. [19] presented a thermal management system model based on electrochemical reactions and thermodynamics, which was validated using the developed experimental system. Their studies can guide the design and optimization of control systems. [PERSON] et al. [20] proposed a control-oriented zero-dimensional (0D) model to investigate temperature variations during load change. Their findings can guide the appropriate coolant mass flow rate and radiator size choices and improve the control capability of the thermal management system. The 0D model has advanced, but components like radiators often lag and overshoot, leading to coolant temperature fluctuation and hysteresis in actual systems. Therefore, combining model and control algorithms is essential [21]. [PERSON] et al. [22] developed a thermal management model for automotive fuel cells with a controller to regulate the fan speed, making the stack temperature range within \(\pm\)0.5 \({}^{\circ}\)C. [PERSON] et al. [23] established a semi-mechanical model based on the thermal manage ment system structure. They proposed three model-based strategies to control the water circulation and fan speed. To achieve reliable performance, [PERSON] et al. [24] proposed a duty ratio split control strategy suitable for automotive fuel cells considering power and optimal temperature. The results indicate that the current governor control strategy is appropriate for on-line implementation with less computational burden. [PERSON] et al. [25] presented a heuristic dynamic programming (HDP) algorithm to design a temperature controller, which effectively improves the stability of the temperature control and the response capability of the system under steady-state conditions. The artificial neural network (ANN) has become one of the most popular data-driven PEMFC models because of its high efficiency in handling complex fuel cell systems [26; 27; 28]. Several ANN models have been proposed for operation optimization and performance prediction of fuel cell systems. [PERSON] and [PERSON] [29] explored an ANN model for the estimation of the current and voltage. The investigation presented models with good predictions. [PERSON] et al. [30] presented an ANN structure with semi-empirical models to seek the optimal operating conditions that maximize the PEMFC efficiency. The ANN model in combination with optimization algorithms has also been studied for PEMFC systems. [PERSON] et al. [31] proposed an ANN model integrated with a genetic algorithm to predict the PEMFC performance and identify its maximum power for operational control. The results demonstrate that the combined ANN-GA method is suitable for predicting fuel cell performance and identifying operation parameters for the maximum powers under various temperatures. Studying the existing research, we found that the scholars usually focus on operation under specified operating parameters, and their research is not well suited to thermal management with complex operating conditions, such as changing load current and preset stack temperature.