## 6 Deployment of the Proposed Approach in Support to Model Building
The others, such as the distance between the plasma boundary and the location of the coils measuring the locked mode, are introduced in [44] for the purpose of deriving a multimachine scaling, which is not the objective of the present study. In three dimensions, it is still possible to apply the proposed methodology of SR via GP with 170 disruptions as examples. Deploying again the probabilistic SVM and the CART ensembles, it has been found that the models provide a good compromise between success rate and false alarms. The methodology described in Section 3 has then been deployed to obtain the equation of the boundary between the safe and disruptive regions of the operational space. The original range of the variables (including disruptive and non-disruptive samples) is: LM \(\epsilon\) [0.0030, 3.1] mT, q95 \(\epsilon\) [2.07, 7.81], li \(\epsilon\) [0.45, 1.64]. The function to be identified  
Figure 7: Plots of the critical value of the locked mode, predicted by Equation (3), versus the various quantities used in the regression for the examples of campaigns C29–C30. Red circles: critical values of the locked mode at the moment of the alarm. Black crosses: critical values of the locked mode 15 ms before the beginning of the current quench. Green circles: critical values of the locked mode at the flat top of the same discharges. Before the beginning of the current quench, the overlap between the values of the locked mode is almost complete. expresses the critical locked mode amplitude as a function of the internal inductance and q95, i.e., f(x,y) = LM(li, q95). The obtained equation reads:  
\[LM=0.475-0.017\cdot q_{95}0^{.95}-0.014\cdot li^{1.00} \tag{4}\]  
with the amplitude of the locked mode signal LM in mT. Here again, only one model is reported for the same reasons adduced in the previous section when discussing relation (1). The plots of Figure 8 show how Equation (4) fits the boundary between the safe and disruptive regions of the operational space. The good quality of the obtained model can be appreciated by inspection of Table 4 for the campaigns C29 and C30 used for the training. Again, to prove the generalisation potential of the derived boundary equation, relation (4) has been applied to the discharges of campaign C31, which are completely new examples never seen by the predictors. The good discrimination capability of the model, shown in Table 5, confirms once more that the methodology proposed manages to converge on an interpretable but preforming equation. The degradation of performance in terms of false alarms is a problem of obsolescence, due to the rapidly varying experimental conditions in C31 and indeed affects in the same way also the ML models. It is worth mentioning that it has been verified that practically the same results can be obtained using the traditional SVM instead of the probabilistic version. Therefore, the results of the investigation  
Figure 8: The boundary between the safe and disruptive regions of the operational space for campaigns C29 and C30. Top left: in the three dimensions LM, \(li\) and q\({}_{95}\). Top right and bottom: the two projections. Blue safe points, red disruptive points. The hypersurface obtained with symbolic regression and non-linearly fitted to the data is shown in green. Only the first disruptive point of each discharge has been reported to help with visualizing the behaviour of the data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Success** & \multirow{2}{*}{**Missed**} & \multirow{2}{*}{**Early**} & \multirow{2}{*}{**Tardy**} & \multirow{2}{*}{**False**} & **Mean** & **Std** \\  & **Rate** & & & & & **(ms)** & **(ms)** \\ \hline \multirow{2}{*}{Equation (4)} & 92.21\% & 3.25\% & 0.65\% & 3.9\% & 11.93\% & 424 & 484 \\  & (142/154) & (5/154) & (1/154) & (6/154) & (52/436) & 424 & 484 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance of Equation (4) for campaign C31. The models obtained at the end of C30 have been applied to the examples of C31 without any retraining.