## 7 Conclusions and Future Prospects  
In this paper, it is shown how it is possible to derive reliably an equation for the boundary between safe and disruptive regions of the operational space directly from the classification provided by machine learning tools. The methodology has been exemplified with two of the most popular types of classifiers, namely SVM and ensembles of CART. The goal is achieved by an original application of Symbolic Regression via Genetic Programming, which proves the further applicability of these techniques compared to previous investigations [29]. Practically the same model is found with either ML tool. The performance of the derived equations, in terms of success rate and false alarms, is practically the same as the original machine learning tools. It can therefore be concluded that the equations, derived by Symbolic Regression via Genetic Programming, match the ones of the machine learning tool models and therefore inherit all their qualities and drawbacks. As a consequence, the critical aspect to obtain valid equations is the quality of the statistical basis used to train the machine learning classifiers. The data driven models, obtained with the methodology described in the paper, clearly outperform by a factor, if not by one order of magnitude, traditional empirical models based on representations such as the Hugill or the beta limit plots. The derived relations for the boundary are also orders of magnitude easier to interpret than the models of the original ML tools. Indeed, traditional SVM for the problem at hand typically comprise hundreds of Gaussian functions centred on an equal number of support vectors. The ensembles of CART classifiers typically require many hundreds of trees to obtain reasonable performances. Therefore, the developed techniques can be tuned to find the best trade-off between complexity and realism; the derived models are of a manageable complexity and, at the same time, do not oversimply the problem at the expenses of poor success rates like the power laws recently proposed. Moreover, by appropriate selection of the Symbolic Regression basis functions, it is possible to obtain equations with physical meaning, which can be compared with theory or used to guide model developments. It is worth emphasizing that the formulation of the equations in a more physically meaningful form does not cause any appreciable reduction in the success rate of classification. Therefore, these equations can be usefully deployed also in real-time networks for the prediction of disruptions. Moreover, a series of exhaustive tests has proved that the proposed methodology can be applied also to the models obtained with adaptive training from scratch of the type reported in [28; 29]. It is important to notice that the analysis presented shows very clearly how, at least in the features space investigated in the paper, the boundary between the safe and disruptive regions of the operational space can have a quite different mathematical form, depending on the number of regressors used. In the case of two independent variables, the equation of the boundary is an exponential whereas in a three-dimensional space becomes a linear equation. This emphasises the importance of the methodology proposed, which does not force _a priori_ the models to have any predefined mathematical form. Moreover, power laws have not proved to be very useful expressions for the boundary on the operational space in JET with the ILW, confirming the preliminary indications reported in [42]. Consequently, the present work confirms the limitations of power laws for the investigation of thermonuclear plasmas, as already reported extensively for the energy confinement time and the radiation limit [46]. With regard to the machine learning aspects of the approach, the methodology described in this work generalises the one pioneered in [26]. SR with GP can be applied nowadays to practically any type of classifier.