## 1 Introduction  
Exhaust emissions from diesel vehicles have long been a major contributor to nitrogen oxides (NOx) in the air, and NOx has been shown to be a serious hazard to both the natural environment and humans [1, 2, 3]. With the introduction of the Euro VII emission regulations [4], more stringent emission standards are about to be implemented, which means that the emission limits for NOx will be further reduced compared to the Euro VI emission regulations. Although exhaust gas recirculation (EGR) can effectively reduce NOx emissions [5], selective catalytic reduction (SCR) is still the most efficient technology to reduce NOx emissions [6, 7, 8]. The SCR system requires the injection of aqueous urea solution during operation, which undergoes hydrolysis to produce ammonia (NH\({}_{3}\)), and which undergoes a reduction reaction with NOx to produce N\({}_{2}\) and H\({}_{2}\)O, catalyzed by a catalyst within the SCR [9]. Although increasing urea injection can improve the NOx conversion efficiency of the SCR system and reduce NOx emissions, excessive urea injection will create more NH\({}_{3}\) slip, and NH\({}_{3}\) jeopardizes the natural environment and human health [10, 11]. In recent years, many have been conducted to improve NOx conversion efficiency, studies such as optimizing the catalyst formulation in SCR and high-pressure SCR spray systems [8; 12]. However, the study of catalysts and SCR structure is usually complicated because it involves the interaction of several aspects, and optimizing only one of these factors not only has a limited effect on the improvement of NOx conversion efficiency, but also requires a large number of bench tests for validation, which consumes time and financial resources. Secondly, prior studies have neglected the effect of NH\({}_{3}\) slip. Currently, in order to improve NOx conversion efficiency as much as possible within the NH\({}_{3}\) emission limits required by the emission regulations, finding an optimization strategy using a mathematical model-based approach is an effective method [13; 14]. [PERSON] et al. studied and developed a time-discretized and space-integrated (TDSI) SCR model with dual temperature-dependent parameters [15]. Their spatial integration model was improved by introducing NH recovery, which improved the accuracy of the model estimation. [PERSON] et al. modeled the transient kinetics of seven different catalysts and developed a model-based catalyst screening strategy to control NOx emissions [16]. [PERSON] et al. developed a comprehensive selective catalytic reduction (SCR) model detailing the global kinetic reactions in the catalyst involving both high and low temperature NH\({}_{3}\) adsorption/desorption sites, as well as low-temperature H\({}_{2}\)O storage for the design and optimization of SCR catalysts [17]. [PERSON] et al. applied a physicochemical model-based Nondominated Sorting Genetic Algorithm II to obtain the desired urea dosage feed ratio and to achieve an optimal trade-off between NOx reduction and NH\({}_{3}\) slip to realize benefits such as improved fuel and urea efficiency [18]. [PERSON] et al. measured the effects of three urea injection parameters--injection velocity, injection angle and droplet size--on NH\({}_{3}\) distribution and wall film formation in a SCR system and optimized the performance of the SCR system using a linear regression model with the help of 2\({}^{3}\) full factorial DoE for multiphase CFD simulations [19]. Although the use of mathematical model-based methods can achieve the prediction of NOx and NH\({}_{3}\) emissions or optimize the control strategy to control NOx emissions, the running time of the model is still a concern due to the large number of factors considered by the mathematical model. The computational volume and complexity of the complex model will increase during the running process, which affects the computational speed of the model [20].