## 1 Disruptions in Tokamaks: An Operational Perspective
To increase the contribution of machine learning tools to the investigation of the physics of global stability in Tokamaks, a new methodology has been devised to reconcile the knowledge acquired by the ML techniques with mathematical expressions of a more traditional form, in terms of interpretable formulas, which can be used both as a guide for analysis developments and as a benchmark of theoretical models. This approach combines the predictive performance and the knowledge discovery capability of ML tools with the necessity to formulate the results in such a realistic way that they can be related to physical theories capable of extrapolation to larger devices. The methodology, to derive physically meaningful models from machine learning tools, consists of the following steps:  
1. Training the machine learning tools for classification, i.e., to discriminate between disruptive and non-disruptive examples;
2. Identifying a sufficient number of points on the boundary between safe and disruptive regions of the operational space on the basis of the models derived by the machine learning tools;
3. Deploying Symbolic Regression via Genetic Programming to express the equation of the boundary in a physically meaningful form, using the points identified in the previous step;
4. Converge on the final model with the help of the Pareto Frontier and non-linear fitting. This procedure for the identification of the disruptive boundary in Tokamaks is an original development proposed here for the first time to the community (a preliminary version of the methodology was introduced in a conference contribution to a completely different audience [26]). In the work presented in this paper, the knowledge discovery tasks rely on Support Vector Machines (SVMs) and ensembles of Classification and Regression Trees (CARTs), whose mathematical background is briefly summarised in the next section. This choice is driven by the need to provide a fully general and sound methodology. In this respect, it should be remembered that SVM and CART ensembles are completely different approaches to learning and give absolutely different types of mathematical models. They are also positioned at quite opposite extremes of the machine learning techniques (see next section): kernel and rule-based methods, respectively. Therefore, the more than satisfactory results reported in this work prove not only the generality of the approach but also increase the confidence in the methodology and conclusions. SVMs are particularly recommended by their good generalisation properties, which guarantee very high success rates, provided the training set is adequate. In addition to traditional Support Vector Machines, the proposed method is also adapted to a probabilistic version of SVM, to show in general how the approach can be particularised for machine learning tools, which provide outputs of this nature. Ensembles of classifiers are a more recent solution, which has been very successful in the development of adaptive predictors [5; 27; 28; 29; 30]. Their basic units, decision trees, are a typical example of rule-based classifiers and constitute a completely different approach to machine learning. The flexibility provided by the ensembles constitutes a very good complement to kernel techniques, such as SVM. To formulate the output of SVM and ensembles of CART in a physically realistic and interpretable way, extensive use is made of Symbolic Regression via Genetic programming; these techniques are therefore covered in Section 2. The actual combination of the various tools, to provide the equation of the boundary between two regions of the operational space, is covered in Section 3. A representative example of the systematic series of numerical tests, performed to prove the potential of the proposed techniques, is reported in Appendix A. JET database with the ITER-like Wall is introduced in Section 4 and the results, in terms of equations for the boundary between the disrupting and non-disruptive regions of the operational space, are the subject of Sections 5 and 6.