## 1 Introduction  
The increasing problems of greenhouse effect and ozone depletion have drawn people's great attentions during the past decades [2; 3; 4; 5]. In the field of heating, ventilation, air conditioning, and refrigeration (HVAC and R) [6; 7; 8], scientists started to use 1,1,1,2,3,3,3-heptafluoropropane (R227 ea) [9; 10; 11] as a substitute in order to replace other refrigerants that are harmful to the ozone (like R114, R12, and R12B1), because R227 ea has a zero ozone depletion potential (ODP) [12]. Other applications of R227 ea include the production of rigid polyurethane foams and aerosol sprays [11; 13]. R227 ea has been shown to be crucial in industrial fields and scientific research. In practical applications, the use of R227 ea requires the exact values of the compressed liquid densities under certain values of temperatures and pressures. However, due to the complexity and uncertainty of the density measurement of R227 ea, precise values of the density are usually difficult to acquire. To solve this problem, molecular dynamic (MD) simulation methods [14; 15; 16] have been used for predicting related thermophysical properties of refrigerants. Nevertheless, these simulation methods have high requirements for computers and require long computational times. Additionally, they need accurate forms of potential energy functions. Motivated by these issues, here, as a typical case study, we aim at finding out alternative modeling methods to help acquire precise values of the densities of R227 ea. Acquiring the density by theoretical conclusion is an alternative approach to replace the MD methods. Equation of state is one of the most popular descriptions of theoretical studies that illustrates the relationship between temperature, pressure, and volume for substances. Based on the recognition that the structure of a liquid is determined primarily by the inner repulsive forces, the Song and Mason equation [17] was developed in the 1990s based on the statistical-mechanics perturbation theories [18; 19] and proved to be available in calculating the densities of various refrigerants recently [20]. However, limitations of the theoretical methods are also apparent. Firstly, the calculated results of refrigerants are not precise enough. Secondly, previous studies only discussed the single result with a given temperature and pressure [20], neglecting the overall change regulation of the density with the changes of temperature and pressure. To find out a better approach that can precisely acquire the density values of R227 ea, here, we first illustrate the three-dimensional change regulation of the density of R227 ea with the changes of temperature and pressure using the Song and Mason equation, and also use novel machine learning techniques [21; 22; 23] to predict the densities of R227 ea based on three groups of previous experimental data [1; 24; 25]. To define the best machine learning methods for the prediction of the densities of R227 ea, different models should be evaluated respectively, which is a necessary comparison process in environmental science. In this case study, support vector machine (SVM) and artificial neural networks (ANNs) were developed, respectively, in order to find out the best model for density prediction. ANNs are powerful non-linear fitting methods that developed during decades, which have good prediction results in many environmental related fields [26; 27; 28; 29; 30]. However, although ANNs usually give effective prediction performances, there is a risk of over-fitting phenomenon [26] if the best number of hidden nodes are not defined, which also indicates that the data size for model training should be large enough. Additionally, the training of ANNs may require relatively long training times if the numbers of hidden nodes are high or the data size is large. Alternatively, SVM, a new machine learning technique developed during these years, has been proved to be effective in numerical predictions for environmental fields [26; 27].