## 1 Introduction  
In recent years, the research on refrigeration and heat pump systems has mainly focused on improving system efficiency, exploring suitable configurations to optimize performance, and identifying optimal control strategies. The performance of refrigeration and heat pump systems depends heavily on the compressor, their core component. Therefore, it is crucial to have an accurate and easy-to-use model for analyzing and predicting compressor performance [1]. Experts and scholars worldwide have extensively researched compressor models to achieve a common goal. There are currently three primary modeling methods in use: the geometry- and physics-based, the empirical, and the semi-empirical methods [2]. Several mathematical models of compressors that use physical and geometric principles have been developed by experts [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. To accurately determine the change in the refrigerant state within the compressor chamber, a range of detailed compressor-related parameters, such as geometric shape, leakage, oil properties, and thermodynamics, must be taken into account. Unfortunately, these models require complex calculations, and obtaining precise data for the compressor can be quite challenging [16]. For the calculation and optimization of compressor performance in refrigeration and heat pump systems, the mathematical models relying on geometric and physical theories are difficult and time-consuming to compute. In such instances, empirical and semi-empirical compressor models are better suited for the task. Among them, empirical models such as (DIN EN 12900:2013, 2013) [17] or (AHRI Standard 540 2015) [18] are more advanced. These models consider mass flow rate and power consumption as third-degree polynomial functions of evaporation and condensation temperatures. However, they are only applicable to fixed compressor speeds. On the other hand, machine learning-based compressor models are relatively popular but require a large amount of experimental data for support [19]. Additionally, empirical models have poor extrapolation capability and may result in significant calculation errors. The reliability of the predictions in varying operating conditions is better with semi-empirical compressor models than with empirical models. Additionally, their computational cost is relatively low, making them more practical for integration into complex system models [1]. LI has established a semi-empirical model for constant-speed scroll compressors based on thermodynamic principles, and the model has been extended to include reciprocating piston compressors. The model calculates refrigerant mass flow rate, discharge temperature, and shaft power, with errors within 5% compared to experimental values [20]. LI has created models for different types of compressors, including variable-speed scroll, reciprocating, and rolling piston compressors. These models have been tested against experimental values, and the errors for calculated refrigerant mass flow rate, shaft power, and discharge temperature are all below 3%. This indicates that the models are highly accurate in predicting these important parameters. [21]. [PERSON] et al. have developed a semi-empirical model that accurately predicts the performance of rolling piston compressors. The model was tested on four different compressors under various operating conditions with different refrigerants. The model's accuracy was verified with calculated errors of within \(\pm\)5% for the refrigerant mass flow rate and compressor power [22]. [PERSON] et al. have developed a theoretical-based explicit calculation model for jet-type variable-speed scroll compressors. The predicted values of the mass flow rate, input power, and discharge temperature have a deviation within \(\pm\)10%, \(\pm\)5%, and \(\pm\)3 K, respectively, compared to the experimental data [23]. A semi-empirical model for reciprocating compressors has been developed by [PERSON] et al.