From machine learning tools to mathematical models: the case of disruption prediction and avoidance

Disruptions remain the most serious issue to be faced by the next generation of Tokamak machines and are also a serious problem for the present largest devices. For example, they are one of the main impediments to systematic high current operation in JET. Given their potential impact on the integrity of the devices, various methods of disruption avoidance and mitigation are being investigated. Of course, reliable prediction tools are a prerequisite to any mitigation or avoidance action. Unfortunately, the theoretical understanding of the causes of disruptions is not sufficient to guarantee reliable predictions. The inadequacies of theoretical and empirical models of disruptions have motivated the development of data driven predictors, some of which, such as APODIS on JET, have shown impressive performance. The main remaining issue with these advanced machine learning tools is now the interpretability. In order to overcome this limitation, a new methodology has been developed to profit from the knowledge, acquired by the machine learning tools, by presenting it in terms of manageable formulas. This approach reconciles the prediction and knowledge discovery capability of machine learning tools with the need to formulate the results in such a way that they can be related to physical theories capable of extrapolation to larger devices. This knowledge discovery step is based on Support Vector Machines (SVM). To formulate the output of SVM in an interpretable way, extensive used is made of Symbolic Regression via Genetic programming. The actual combination of the two methods provides the equation of the boundary between two regions of operational space, safe and disruptive. The potential of the method is illustrated by examples using JET database with the new ITER Like Wall.