## 6 Deployment of the Proposed Approach in Support to Model Building
The values of the critical locked mode has been calculated with model (3) with the values of the parameters suggested in [45] at the following times: at the time slice of the alarm (when the experimental locked mode reaches the critical value predicted by the equation) and 15 ms before the beginning of the current quench. The estimates of the critical threshold have also been calculated for the flat top phase of the same discharges. From the plots reported, it can be easily seen that, before the beginning of the current quench, there is full overlap between the estimates for the flat top and the pre-disruptive time slices. Therefore, these estimates are not useful for prediction. This has been verified by testing the performance of the critical value of the locked mode proposed in [44] for the entire C29-C30 campaigns (for a total of 170 disruptive shots and 987 safe discharges). Again, all the time slices with plasma current higher than 750 kA have been included in the analysis. The final statistics are reported in Tables 3 and 4, from which it can be appreciated how the success rate is certainly less than satisfactory. Even if Equation (3) does not seem to provide very useful information for prediction in JET with the ILW, at least for the campaigns analysed, the set of quantities proposed contains signals, which are unquestionably very important. In particular the locked mode and the internal inductance have proved to be essential also in the analysis reported in Section 5. Therefore, it can be argued that it is the power law form of Equation (3), which is not adequate to model JET data. The probabilistic SVM and the CART ensembles have therefore been applied to the regressors used in Equation (3) to derive the critical value of the locked mode signal. The models derived present very good performance; the success rate is about 95% and the false alarms are 5% again for a comfortable range of threshold probabilities. Therefore, the ML models perform slightly worse than the one of Equation (1) but are very competitive. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Success Rate** & **Missed** & **Early** & **Tardy** & **False** & **Mean** & **Std** \\  & & & & & & **(ms)** & **(ms)** \\ \hline Equation (4) & 91.7\% (156/170) & 1.2\% (2/170) & 0\% (0/170) & 7.1\% (12/170) & 2.3\% (23/987) & 338 & 357 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of Equation (4) for Campaigns C29–C30. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Success Rate** & **Missed** & **Early** & **Tardy** & **False** & **Mean** & **Std** \\  & & & & & & **(ms)** & **(ms)** \\ \hline Equation (3) & 52.35\% (89/170) & 24.12\% (41/170) & 0\% (0/170) & 23.53\% (40/170) & 1.72\% (17/987) & 175 & 328 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The traditional figures of merit to assess the performance of predictors for the case of Equation (3) applied to campaigns C29–C30. The main reason for the better performance of the machine learning models, compared to Equation (3), resides as expected in the functional form of the final equations: the machine learning tools are not limited to power laws. Unfortunately, the technique proposed in this paper, to convert ML models into realistic equations, is not viable for such a high number of regressors. Indeed, the dimensionality of Equation (3) is too high and the number of disruptions insufficient (by orders of magnitude). In such a number of dimensions, the points are too sparse in the hyperspace and it is not possible to reconstruct robustly and reliably the boundary. This is not a limitation of the methodology but a consequence of the excessive sparsity of the available data (the so-called curse of dimensionality). On the other hand, the number of really relevant quantities for JET is three: locked mode, internal inductance and q95.