## 5 A Data-Driven Model for JET with the ILW
The methodology, described in Section 3, has then been applied to the SVM model and the CART ensembles, to obtain a manageable equation of the boundary. After the analysis performed with  
Figure 5: Plot of the safe and disruptive regions of the operational space in JET with the ILW according to the Support Vector Machine (SVM). The colour code represents the posterior probability of the classifier. The black circles are all the non-disruptive shots (10 random time slices for each shot). The red asterisks are the data of the disruptive shots at the time slice when the predictor triggers the alarm. The light blue squares are the false alarms. In red is the 80% disruption probability. Figure 6: Plot of the safe and disruptive regions of the operational space in JET with the ILW according to the SVM. The colour code represents the posterior probability of the classifier. The black circles are all the non-disruptive shots (10 random time slices for each shot). The red asterisks are the data of the disruptive shots at the time slice when the predictor triggers the alarm. The light blue squares are the false alarms. In red is the 80% disruption probability. the Pareto Frontier, the following equation has been retained as a reasonable compromise between complexity and accuracy:  
\[LM(l_{i})=a_{0}\exp\Bigl{(}a_{1}l_{i}^{a_{2}}\Bigr{)} \tag{1}\]  
where \(LM\) is the amplitude of the locked mode expressed in \(10^{-4}\) Tesla, \(l_{i}\) the internal inductance and the coefficients assume the values:  
\[ \begin{split} a_{0}=5.4128\pm 0.0031;\\ a_{1}=-0.11614\pm 0.00085;\\ a_{2}=2.21\pm 0.011;\end{split}  \tag{2}\]  
A quick comment is required to explain how a single equation has been derived from the deployment of two ML classifiers. The analysed database is so large and consistent that, with the help of the Pareto Frontier, both the probabilistic SVM and the CART ensemble identify the same mathematical form, the exponential Equation (1), for the model as a good compromise between complexity and goodness of fit. At this point, the procedure requires optimising the parameters of the model with nonlinear fitting. This step has been particularised for the probabilistic SVM, which originally presented slightly higher performances (see Table 1). In any case, it has been checked that repeating the step for the CART ensemble would produce practically the same results, within the confidence intervals of the models and therefore without any appreciable difference for the aspects discussed in the rest of the paper. The performance of relation (1), in terms of the usual figures of merit adopted to qualify predictors, is reported in the third row of Table 1, from which it emerges clearly how this equation reproduces quite effectively the quality of the original models, obtained with the probabilistic SVM and the CART ensembles. In graphical terms, Equation (1) is shown in red in both Figures 5 and 6. From the plots of these figures, it is easy to appreciate how the analytical formula obtained with the proposed methodology follows quite effectively the curve level of the ML classifiers. To confirm the validity of the equation derived by SR via GP, Equation (1) has been applied to the discharges of the entire next campaign C31. From the results reported in Table 2, it is clear that Equation (1) is very robust; it manages to preserve a very good performance for the entire following campaign. A small degradation in performance is physiological, because the operational space changes significantly during an entire campaign on JET, particularly now with the new ILW. It is also important to notice that the model derived by SR via GP shows practically the same performance as the SVM and CART ensemble models, confirming that the proposed approach has managed to identify properly the equation of the boundary derived by the ML classifiers. Therefore, it is reasonable to expect that all the good properties of the SVM and CART ensemble models (robustness, generalisation capability, etc.)