## 1 Introduction  
The global automotive industry has undergone a period of rapid growth due to social development. Data provided by the Automobile Industry Association [1] show that car ownership in China will increase to 500 million by 2030. Although the rapid development of the automobile industry has made people's lives convenient, it has caused energy and environmental problems. Automobile exhaust has become the main source of atmospheric pollution in cities and continues to threaten the health of urban residents. The main pollutants in vehicle exhaust are HC, NO\({}_{\mathcal{K}}\), CO, and particulate matter (PM) [2]. PM contains many harmful substances that stay permanently in the atmosphere. Therefore, its impact on human health and atmospheric quality has elicited much concern [3]. Means to improve the fuel economy, combustion, and emission performance of internal combustion engines have consistently been a key issue. Gasoline engine energy utilization is approximately 30% lower than the energy utilization of diesel engines. To improve the thermal efficiency of gasoline engines, scholars have extensively investigated gasoline direct injection (GDI) technology in the field of internal combustion engines [4; 5; 6]. Although GDI technology can improve the thermal efficiency of gasoline engines, the time of fuel and air mixing is shortened, leading to partial uneven mixing and serious PM emission problems [7]. Therefore, the main problem is improving the thermal efficiency and reducing the PM emissions of GDI engines [8; 9]. Traditional diesel engines use high-pressure injection to form a non-uniform mixture of fuel and air for diffusion combustion. The heat release rate is determined by the mixing rate of fuel and air in the diffusion combustion stage. Fuel and air are mixed unevenly due to the short mixing time and low fuel diffusion rate in air. This situation results in the production of large amounts of soot in the high-temperature anoxic zone and increased soot emissions during combustion. Soot emission reduction is thus a major problem in diesel engines. Given the low thermal efficiency of GDI engines and high soot emission of diesel engines, scholars established a method to achieve high temperature and pressure in the combustion chamber during engine operation; this high-temperature and high-pressure environment is called the supercritical environment of fuel [10]. Fuel can rapidly form a homogeneous mixture with air for combustion and heat release due to the low surface tension, low viscosity, and large diffusion coefficient of supercritical fuel. This feature helps reduce the uneven distribution of concentration in the cylinder so that fuel can be completely burned and thermal efficiency can be improved. Supercritical-state fuel can evaporate directly without phase change. As a result, the formation of the mixture within the cylinder is accelerated, and fuel and air are uniformly mixed before combustion. Supercritical-state fuel is conducive for premixed combustion and improves combustion efficiency. In addition, in the diffusion combustion stage, supercritical fuel can be quickly mixed with air because of the large diffusion coefficient of this fuel. Thus, the reactant concentration becomes uniform, and the heat release rate is improved. Supercritical-state fuel can be combined with the latest injection technology to further control the combustion process, thereby reducing the emissions of pollutants and optimizing the combustion performance of engines. The development of supercritical fuel combustion technology requires reliable data on fuel properties. Surrogate models are commonly used to estimate the chemical and physical properties of real fuels because the composition of fuels is highly complicated and lacks corresponding experimental data. In their study on dieseline, [PERSON] et al.