## Appendix A  
The procedure, described in this paper, to obtain manageable equations from the models outputted by machine learning classifier, has been subjected to a systematic series of numerical tests. The results have always been positive, and the proposed technique has typically allowed recovering the original equations describing the boundary between the two classes. In the following, the algorithms for these numerical tests are described in detail.  
The main sequence of operations, to produce synthetic data to test the methodology, consists of the following six steps:  
1. Definition of an initial function for the boundary;
2. Generating samples of the two classes from the function;
3. Training the SVM for classification;
4. Building an appropriate mesh on the domain;
5. Determining a sufficient number of points on the hypersurface identified by the SVM;Deploying symbolic regression to obtain the equation of the hypersurface from the points previously generated.  
In the case of probabilistic SVM or CAR ensembles, points 4 and 5 collapse to a single, very easy step, since it is possible to directly obtain the points at the required level of probability directly from the machine learning tool.  
In the rest of this Appendix, more details about this procedure are provided. To fix the ideas, the discussion is particularised for the case of traditional SVM, which is the most complex alternative. Moreover, the reported example can be considered of the same level of complexity as the actual problem discussed in the following sections, namely the determination of the disruptive region in terms of traditional signals available in real time. To this end, a five-dimensional synthetic database has been generated with the characteristics described in Table 11.  
Then the traditional procedure for finding the best parameters of the SVM, \(\gamma\) and the standard deviation of the kernel, has been applied and the best values identified [26; 27]. The final accuracies of classification for the train and test data are presented in Table 12.  
After generating the grid and finding the hypersurface points, SR via GP has been applied and the following expression for the hypersurface has been obtained:  
\[y=0.9334\ sin\ (0.9190(x_{1}+x_{2}))-0.5010\ x_{3}\ x_{4} \tag{11}\]  
The obtained equation is in good agreement with the initial function, reported in Table 11. The quality of this estimate can be confirmed by comparing the success rate of the SVM and of the equation found by SR via GP. The classification success rate of the equation found with SR is reported in Table 13 (to be compared with the results reported in Table 12).  
\begin{table}
\begin{tabular}{c c} \hline
**Database Type** & **Classification Accuracy in Percent** \\ \hline Train Data & 96.1337 \\ \hline Test data & 96.0422 \\ \hline \end{tabular}
\end{table}
Table 12: The accuracies obtained by the SVM for the train and test sets, by classifying the synthetic database with database with the best sigma that equals to 0.6.  
\begin{table}
\begin{tabular}{c c} \hline
**Steps** & **Values** \\ \hline Initial Function & y = sin(x\({}_{1}+x_{2})-0.5\ x_{3}\ x_{4}\) \\ \hline Ranges of Variables & \(-1.5<x_{1}<1.5\) and \(-2<x_{2}<2\) \\  & \(0<x_{3}<2\) and \(2<x_{4}<4\) \\ \hline Number of Points for Each Class & 2000 \\ \hline Offset & 10\% of y domain \\ \hline Classification Noise & \(\sim\)5\% \\ \hline \end{tabular}
\end{table}
Table 11: Settings for testing SVM–GP on a five-dimensional synthetic database.  
From the comparison of the success rates obtained via SVM and with the derived mathematical equations, it can be concluded that the SVM-GP method has excellent performance for interpreting the SVM hyperplane as a hypersurface equation.