## 3 Results and Discussion  
### Recognition of Flow Patterns  
The paper studied the ML model accuracy by inputting the primitive parameters and the dimensionless numbers. Before computing, all data from both Experiment 1 and 2 had been divided into the training and testing data by the ratio of 4:1, whatever they were in the solution sets with dimensionless numbers (Set1, Set2, and Set3) or primitive parameters (Set4). The training data were to establish the prediction model and the testing data were to verify the model accuracy. The accuracy of flow pattern prediction was the ratio of the number of predicted samples in the test set to the number of all samples. After the data partition, the SVM algorithm recognized the four flow patterns with different accuracy in both experiments (Figure 3). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Dimensionless Numbers**} & \multicolumn{2}{c}{**Primitive Parameters**} \\ \hline Equation & & \(F(W_{c},h_{c},W_{d},h_{d},W_{out},h_{out},X,\) \\  & & & \(F(W_{c},h_{c},W_{d},h_{d},W_{out},h_{out},  
It can be seen from Figure 3a that all prediction models from the solution sets with both dimensionless and primitive parameters had a similar accuracy fluctuating within the range from 80.6% (Set1) to 86.6% (Set4) in Experiment 1. On three solution sets with dimensionless numbers, the prediction accuracy in Set1, Set2, and Set3 possessed 4, 3, and 4 dimensionless numbers as the input variables in Figure 3, respectively. Set4 with the primitive parameters had six input variables higher than those in Set1, Set2, and Set3. It was interesting that all the prediction accuracies in the four solution sets were very close. This indicated that, for the recognition of flow patterns, the SVM algorithm inputting the dimensionless numbers minimized the specimen information loss, reduced the amount of computation, and maintained the model accuracy simultaneously. Figure 3b gives similar results in Experiment 2. The recognition accuracy is nearly consistent, about 93% in all solution sets. All dimensions of input variables are the same (4 dimensions) in both dimensionless and primitive parameters. Compared with Experiment 1, the recognition accuracy of flow patterns in Experiment 2 is higher, about 10%. Figure 3 also proves that the recognition of flow patterns with dimensionless numbers has not decreased the model accuracy and not lost information compared with primitive parameters. Figure 4 reveals the recognition accuracy difference between Experiment 1 and Experiment 2, taking Set2, for example. Set2 has 3 dimensionless numbers of \(\pi_{7}\), \(\pi_{10}\), and \(\pi_{12}\) (Table 3) governed by three parameters of \(\alpha,Re_{c}\), and \(We_{d}\) (Table 2) in Experiment 1. Setting \(\alpha\), \(Re_{c}\), and \(We_{d}\) as the coordinate axis, Figure 4a plots the distribution map of four flow patterns in Experiment 1. It is true that the boundaries among the different flow patterns are crossed and not clear with \(\alpha\) changing. Figure 4: \(Cont.\)  
Figure 3: The recognition accuracy of flow patterns by SVM algorithm, (**a**) Experiment 1: gas-liquid two-phase flow, (**b**) Experiment 2: liquid-liquid two-phase flow. In Experiment 2, the dimensionless numbers of \(\pi_{6}\),\(\pi_{7}\),\(\pi_{10}\), and \(\pi_{12}\) (Table 3) in Set2 are controlled by four parameters of \(X/W_{out}\), \(\alpha\), \(Re_{c}\), and \(We_{d}\) (Table 2). Setting \(\alpha\), \(Re_{c}\) and \(We_{d}\) as the coordinate axis and \(X/W_{out}\), \(Re_{c}\), and \(We_{d}\) as the coordinate axis, respectively, the distribution maps of four flow patterns are drawn in Figure 4b. At each layer with a different \(\alpha\) or \(X/W_{out}\) value, the boundaries among the different flow patterns are very clear without any crossing. Back to the classification task, the distinguished boundary between different data often benefits to realize the classification solution easily.