## 3 Results
### Combination of the Best \(Se\)  
Based on the results obtained on the test dataset, the five SEs with the best estimation accuracy were selected. In Table 7, the results of the best SEs that were selected are marked with red color. The main criterion for choosing the SEs was that the \(\overline{R}^{2}\) score was higher than 0.989. The chosen SEs can be written in the following form:  
\[y_{1} = -14.061\Big{(}\big{|}\sin(\sqrt{\sqrt{\frac{\min(\sin(X_{1}), \sqrt[3]{X_{0}})}{\sqrt{X_{9}}}}})-\min(-X_{18}  
\[+ X_{1}(\sqrt[3]{X_{0}-2345.71}-X_{2})+\sqrt{\cos(X_{2})}+X_{4})+X_{0},\] \[y_{5} = -\max(7.64(X_{1}+X_{3}),0.43\log(\min(\Big{(}X_{2}|\min(221.844X_{2} \cot(\cos(X_{2})),-9574.83\] \[\min(8546.04(X_{1}+X_{3}),X_{8}(X_{0}+X_{1}+\min((2X_{0}+X_{1})X_{8 },1529.14(1529.14(X_{1}+X_{17})\] \[- (2X_{0}+X_{1})X_{8})))))|\Big{)}\Big{/}\big{(}|X_{1}+\sqrt[3]{| \cos(X_{2})|}|\big{)},0.43\log(\sqrt[9]{\sin(\max(\sqrt{X_{0}},\sqrt[3]{X_{4}} )))))))\] \[+ |\min(7.33(X_{1}+X_{3}),X_{8}(X_{0}+X_{1}+|\cos(X_{2})|))|-21.09.\]  
However, it should be noted that, to use Equations (3)-(7) the values of input variables must be scaled using the StandardScaler method. In Equations (3)-(7), the mathematical functions such as the square root, natural logarithm, logarithm with base 2 and 10, and division function are specifically defined to avoid complex, infinite values or zero division errors. The definition of these functions is given in Appendix A.  
The analysis of Equations (3)-(7) showed that, using all five SEs together to compute the output all 19 variables is required. However, if Equations (3)-(7) are used individually, not all input variables are required. To compute the output in Equation (3), 13 out of 19 input variables are required. The variables that are required to compute the output are \(X_{0}\),...,\(X_{9}\), \(X_{15}\), \(X_{17}\), and \(X_{18}\). It is evident from Table 2 that these variables are PBstart, PCstart, PDstart, PFstart, PArise, PBrise, PCrise, PDrise, PFrise, PAfall, PBwidth, PCwidth, and PFwidth, respectively. The total number of variables required to compute the output using Equation (4) is 10 out of 19, and these variables are \(X_{1}\),...,\(X_{6}\), \(X_{8}\), \(X_{14}\), \(X_{15}\), and \(X_{18}\). From Table 2, these input variables are PCstart, PDstart, PFstart, PArise, PBrise, PCrise, PFrise, PAwidth, PBwidth, and PFwidth, respectively. In Equation (5), to compute the output, the 12 out of 19 input variables required are \(X_{0}\),..., \(X_{8}\), \(X_{14}\), \(X_{16}\), and \(X_{18}\). These variables are PBstart, PCstart, PDstart, PFstart, PArise, PBrise, PCrise, PDrise, PFrise, PAwidth, PCwidth, and PFwidth, respectively. All input variables are required to compute the output using Equation (6). The lowest number of input variables (7) is required to compute the output when Equation (7) is used. Equation (7) consist of \(X_{0}\),...,\(X_{4}\), \(X_{8}\), and \(X_{17}\), and from Table 2, these variables are PBstart, PCstart, PDstart, PFstart, PArise, PFrise, and PDwidth.  
The set of previously shown SEs was evaluated on the entire dataset, and the results are presented in Figure 8 and Table 8.  
Figure 8: The graphical representation of the performance metric values obtained with the best combination of SEs on the entire dataset. \(\sigma\) is shown in the case of the total mean values in the form of an error bar.  
The results shown in Table 8 showed that, using a customized combination of the SEs, even higher estimation accuracy was achieved. The mean values were better than those shown in Table 7, and the \(\sigma\)s were smaller.  
The reconstruction of the interaction locations was performed in [13], where the authors used the DNN. For the evaluation of the results, the authors used the \(RMSE\), and the lowest achieved value was 1.53. If these results are compared to the results shown in Table 8, it can be seen that the proposed method outperformed the results in [13].