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In the last years, it has become apparent that detecting disruptions with sufficient anticipation time is an essential but not exclusive task of predictors. It is also important that the prediction is accompanied by appropriate qualifications of its reliability and it is formulated in mathematical terms appropriate for the task at hand (mitigation, avoidance, classification etc.). In this paper, a wide series of rule-based predictors, of the Classification and Regression Trees (CART) family, have been compared to assess their relative merits. An original refinement of the training, called noise-based ensembles, has allowed not only to obtain significantly better performance but also to increase the interpretability of the results. The final predictors can indeed be represented by a tree or a series of specific and clear rules. Such performance has been proved by analysing large databases of shots on JET with both the carbon wall and the ITER Like Wall. In terms of performance, the developed tools are therefore very competitive with other machine learning techniques, with the specificity of formulating the final models in terms of trees and simple rules.

Understanding the details of the correlation between time series is an essential step on the route to assessing the causal relation between systems. Traditional statistical indicators, such as the Pearson correlation coefficient and the mutual information, have some significant limitations. More recently, transfer entropy has been proposed as a powerful tool to understand the flow of information between signals. In this paper, the comparative advantages of transfer entropy, for determining the time horizon of causal influence, are illustrated with the help of synthetic data. The technique has been specifically revised for the analysis of synchronization experiments. The investigation of experimental data from thermonuclear plasma diagnostics proves the potential and limitations of the developed approach. For complete list of authors see http://dx.doi.org/10.3390/e20090627

Understanding the many aspects of tokamak physics requires the development of quite sophisticated models. Moreover, in the operation of the devices, prediction of the future evolution of discharges can be of crucial importance, particularly in the case of the prediction of disruptions, which can cause serious damage to various parts of the machine. The determination of the limits of predictability is therefore an important issue for modelling, classifying and forecasting. In all these cases, once a certain level of performance has been reached, the question typically arises as to whether all the information available in the data has been exploited, or whether there are still margins for improvement of the tools being developed. In this paper, a theoretical information approach is proposed to address this issue. The excellent properties of the developed indicator, called the prediction factor (PF), have been proved with the help of a series of numerical tests. Its application to some typical behaviour relating to macroscopic instabilities in tokamaks has shown very positive results. The prediction factor has also been used to assess the performance of disruption predictors running in real time in the JET system, including the one systematically deployed in the feedback loop for mitigation purposes. The main conclusion is that the most advanced predictors basically exploit all the information contained in the locked mode signal on which they are based. Therefore, qualitative improvements in disruption prediction performance in JET would need the processing of additional signals, probably profiles.

Control of instabilities such as ELMs and sawteeth is considered an important ingredient in the development of reactor-relevant scenarios. Various forms of ELM pacing have been tried in the past to influence their behavior using external perturbations. One of the main problems with these synchronization experiments resides in the fact that ELMs are periodic or quasi-periodic in nature. Therefore, after any pulsed perturbation, if one waits long enough, an ELM is always bound to occur. To evaluate the effectiveness of ELM pacing techniques, it is crucial to determine an appropriate interval over which they can have a real influence and an effective triggering capability. In this paper, three independent statistical methods are described to address this issue: Granger causality, transfer entropy and recurrence plots. The obtained results for JET with the ITER-like wall (ILW) indicate that the proposed techniques agree very well and provide much better estimates than the traditional heuristic criteria reported in the literature. Moreover, their combined use allows for the improvement of the time resolution of the assessment and determination of the efficiency of the pellet triggering in different phases of the same discharge. Therefore, the developed methods can be used to provide a quantitative and statistically robust estimate of the triggering efficiency of ELM pacing under realistic experimental conditions.

Prediction is one of the main objectives of scientific analysis and it refers to both modelling and forecasting. The determination of the limits of predictability is an important issue of both theoretical and practical relevance. In the case of modelling time series, reached a certain level in performance in either modelling or prediction, it is often important to assess whether all the information available in the data has been exploited or whether there are still margins for improvement of the tools being developed. In this paper, an information theoretic approach is proposed to address this issue and quantify the quality of the models and/or predictions. The excellent properties of the proposed indicator have been proved with the help of a systematic series of numerical tests and a concrete example of extreme relevance for nuclear fusion.

Determination of causal-effect relationships can be a difficult task even in the analysis of time series. This is particularly true in the case of complex, nonlinear systems affected by significant levels of noise. Causality can be modelled as a flow of information between systems, allowing to better predict the behaviour of a phenomenon on the basis of the knowledge of the one causing it. Therefore, information theoretic tools, such as the transfer entropy, have been used in various disciplines to quantify the causal relationship between events. In this paper, Transfer Entropy is applied to determining the information relationship between various phenomena in Tokamaks. The proposed approach provides unique insight about information causality in difficult situations, such as the link between sawteeth and ELMs and ELM pacing experiments. The application to the determination of disruption causes, and therefore to the classification of disruption types, looks also very promising. The obtained results indicate that the proposed method can provide a quantitative and statistically sound criterion to address the causal-effect relationships in various difficult and ambiguous situations if the data is of sufficient quality.