## 1 Introduction  
Solar energy, one of the clean energies with the largest source on the planet's surface, has attracted increasing attention due to the enormous challenges of climate change and resource depletion. Concentrated solar power (CSP), one of the well-established solar energy technologies [1; 2; 3], has added almost 0.6 TWh of CSP generation from 2019 to 2020. However, based on the report of IEA, to achieve net zero power CSP generation of 204 TWh in 2030, the additions are much lower than required [4]. Therefore, huge efforts are urgently demanded to increase the efficiency of the CSP thermal system. Parabolic trough collectors (PTC), as one of the commercial CSP technologies [5; 6; 7; 8], have become a research hotspot. The PTC commonly consists of mirrors with a curved shape and an absorber tube. The former serves to concentrate the solar energy on the latter, then the circulation inside the tube is heated up, and the generated steam turns a turbine for electricity. The absorber tube is usually made of steel, which is a good conductor of heat. To reduce its thermal loss, a concentric glass envelope is employed. Furthermore, the space between the glass envelope and the steel tube can be under a vacuum for better isolation. Therefore, to enhance the heat transfer performance of the absorber tube, there are usually two ways: one consideration is to improve the conductivity of the working fluid, for which nanofluids are commonly used; the other concentrates on the shape modification of the tube to increase the turbulence and consequently to enhance the heat transfer, such as using inserts and fins. A huge volume of papers has been published to describe the PTC performance enhancement by using nanofluids [9; 10; 11; 12; 13; 14]; the total number is 34,230 from 2010 to 2021 [9]. According to the review [12], the most significant nanofluids are 8% Al\({}_{2}\)O\({}_{3}\)/Syltherm 800, which can achieve an increment of 76% in heat transfer coefficient [15]. Furthermore, studies are not limited to mono nanofluids; hybrid nanofluids have also attracted scientists' attention due to the superior thermal characteristics and stability [16; 17; 18; 19], which are even better than mono nanofluids. At the same time, a considerable amount of literature has been published to investigate the influence of various fins on the performance of PTC absorber tubes as well. [PERSON] et al. [20; 21] reported two investigations of PTC absorber tubes, both with eight internal rectangular longitudinal fins around the tube. Twelve cases with different fin lengths and thicknesses were tested and compared with the smooth case. Based on various criteria, the optimal case is not the same. Unlike [PERSON] et al., [PERSON] et al. [22] proposed the longitudinal fins in the lower half of the receiver tube, which receives most of the reflection of the sun. Twelve of the same cases with [PERSON] et al. were investigated, and the results showed that the fin with the length of 15 mm and the thickness of 6 mm is optimal. Another part of the literature proposed different shapes for fins, such as a triangle fin [23; 24], a trapezoidal fin [24], pin fin arrays [25], and a fin coupled with insert [26]. These studies focused more on comparing the efficiency of new PTC tubes to the reference smooth tube and did not carry out the analysis on fin-shape parameters. Most of the above studies investigated the influence of the nanofluids and fin-shape parameters on the thermal performance of absorber tubes. Therefore, many numerical simulations have been performed, which have required huge computational resources. Furthermore, this problem occurs in other parametrical studies as well [27; 28]. Fortunately, these burden calculations could be avoided by profiting from the machine learning or deep learning methods, which show great potential in building a reduced-order model (ROM) for highly nonlinear problems.