Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 Nucl. Fusion 39 2137-2664), is reviewed. Recent theoretical and experimental research has made important advances in both understanding and control of MHD stability in tokamak plasmas. Sawteeth are anticipated in the ITER baseline ELMy H-mode scenario, but the tools exist to avoid or control them through localized current drive or fast ion generation. Active control of other MHD instabilities will most likely be also required in ITER. Extrapolation from existing experiments indicates that stabilization of neoclassical tearing modes by highly localized feedback-controlled current drive should be possible in ITER. Resistive wall modes are a key issue for advanced scenarios, but again, existing experiments indicate that these modes can be stabilized by a combination of plasma rotation and direct feedback control with non-axisymmetric coils. Reduction of error fields is a requirement for avoiding non-rotating magnetic island formation and for maintaining plasma rotation to help stabilize resistive wall modes. Recent experiments have shown the feasibility of reducing error fields to an acceptable level by means of non-axisymmetric coils, possibly controlled by feedback. The MHD stability limits associated with advanced scenarios are becoming well understood theoretically, and can be extended by tailoring of the pressure and current density profiles as well as by other techniques mentioned here. There have been significant advances also in the control of disruptions, most notably by injection of massive quantities of gas, leading to reduced halo current fractions and a larger fraction of the total thermal and magnetic energy dissipated by radiation. These advances in disruption control are supported by the development of means to predict impending disruption, most notably using neural networks. In addition to these advances in means to control or ameliorate the consequences of MHD instabilities, there has been significant progress in improving physics understanding and modelling. This progress has been in areas including the mechanisms governing NTM growth and seeding, in understanding the damping controlling RWM stability and in modelling RWM feedback schemes. For disruptions there has been continued progress on the instability mechanisms that underlie various classes of disruption, on the detailed modelling of halo currents and forces and in refining predictions of quench rates and disruption power loads. Overall the studies reviewed in this chapter demonstrate that MHD instabilities can be controlled, avoided or ameliorated to the extent that they should not compromise ITER operation, though they will necessarily impose a range of constraints.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S03/pdf

Chapter 3: MHD stability, operational limits and disruptions

Climate change is one of the greatest challenges facing humanity, and we, as machine learning experts, may wonder how we can help. Here we describe how machine learning can be a powerful tool in reducing greenhouse gas emissions and helping society adapt to a changing climate. From smart grids to disaster management, we identify high impact problems where existing gaps can be filled by machine learning, in collaboration with other fields. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the machine learning community to join the global effort against climate change.

Tackling Climate Change with Machine Learning

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Plasma Physics and Controlled Fusion Conference: Focussing on Tokamak Research

Nuclear fusion power delivered by magnetic-confinement tokamak reactors holds the promise of sustainable and clean energy1. The avoidance of large-scale plasma instabilities called disruptions within these reactors2,3 is one of the most pressing challenges4,5, because disruptions can halt power production and damage key components. Disruptions are particularly harmful for large burning-plasma systems such as the multibillion-dollar International Thermonuclear Experimental Reactor (ITER) project6 currently under construction, which aims to be the first reactor that produces more power from fusion than is injected to heat the plasma. Here we present a method based on deep learning for forecasting disruptions. Our method extends considerably the capabilities of previous strategies such as first-principles-based5 and classical machine-learning7–11 approaches. In particular, it delivers reliable predictions for machines other than the one on which it was trained—a crucial requirement for future large reactors that cannot afford training disruptions. Our approach takes advantage of high-dimensional training data to boost predictive performance while also engaging supercomputing resources at the largest scale to improve accuracy and speed. Trained on experimental data from the largest tokamaks in the United States (DIII-D12) and the world (Joint European Torus, JET13), our method can also be applied to specific tasks such as prediction with long warning times: this opens up the possibility of moving from passive disruption prediction to active reactor control and optimization. These initial results illustrate the potential for deep learning to accelerate progress in fusion-energy science and, more generally, in the understanding and prediction of complex physical systems. Using data from plasma-based tokamak nuclear reactors in the US and Europe, a machine-learning approach based on deep neural networks is taught to forecast disruptions, even those in machines on which the algorithm was not trained.

Predicting disruptive instabilities in controlled fusion plasmas through deep learning

A survey has been carried out into the causes of all 2309 disruptions over the last decade of JET operations. The aim of this survey was to obtain a complete picture of all possible disruption causes, in order to devise better strategies to prevent or mitigate their impact. The analysis allows the effort to avoid or prevent JET disruptions to be more efficient and effective. As expected, a highly complex pattern of chain of events that led to disruptions emerged. It was found that the majority of disruptions had a technical root cause, for example due to control errors, or operator mistakes. These bring a random, non-physics, factor into the occurrence of disruptions and the disruption rate or disruptivity of a scenario may depend more on technical performance than on physics stability issues. The main root cause of JET disruptions was nevertheless due to neo-classical tearing modes that locked, closely followed in second place by disruptions due to human error. The development of more robust operational scenarios has reduced the JET disruption rate over the last decade from about 15% to below 4%. A fraction of all disruptions was caused by very fast, precursorless unpredictable events. The occurrence of these disruptions may set a lower limit of 0.4% to the disruption rate of JET. If one considers on top of that human error and all unforeseen failures of heating or control systems this lower limit may rise to 1.0% or 1.6%, respectively.

http://iopscience.iop.org/article/10.1088/0029-5515/51/5/053018/pdf

Survey of disruption causes at JET

Disruptions are sudden and unavoidable losses of confinement that may put at risk the integrity of a tokamak. However, the physical phenomena leading to disruptions are very complex and non-linear and therefore no satisfactory model has been devised so far either for their avoidance or their prediction. For this reason, machine learning techniques have been extensively pursued in the last years. In this paper a real-time predictor specifically developed for JET and based on support vector machines is presented. The main aim of the present investigation is to obtain high recognition rates in a real-time simulated environment. To this end the predictor has been tested on the time slices of entire discharges exactly as in real world operation. Since the year 2000, the experiments at JET have been organized in campaigns named sequentially beginning with campaign C1. In this paper results from campaign C1 (year 2000) and up to C19 (year 2007) are reported. The predictor has been trained with data from JET’s campaigns up to C7 with particular attention to reducing the number of missed alarms, which are less than 1%, for a test set of discharges from the same campaigns used for the training. The false alarms plus premature alarms are of the order of 6.4%, for a total success rate of more than 92%. The robustness of the predictor has been proven by testing it with a wide subset of shots of more recent campaigns (from C8 to C19) without any retraining. The success rate over the period between C8 and C14 is on average 88% and never falls below 82%, confirming the good generalization capabilities of the developed technique. After C14, significant modifications were implemented on JET and its diagnostics and consequently the success rates of the predictor between C15 and C19 decays to an average of 79%. Finally, the performance of the developed detection system has been compared with the predictions of the JET protection system (JPS). The new predictor clearly outperforms JPS up to about 180 ms before the disruptions.

https://iopscience.iop.org/article/10.1088/0029-5515/50/2/025005/pdf

An advanced disruption predictor for JET tested in a simulated real-time environment

Experiments have established the regions of parameter space in JET that lead to runaway generation in disruptions. Previous measurements on the structure of the runaway beam have been confirmed. The delay in runaway generation following temperature collapse is found to be caused by the very high density generated by the disruption. It is shown that runaway generation in JET can be best modelled and understood by including avalanche processes.

http://iopscience.iop.org/article/10.1088/0029-5515/42/8/312/pdf

Behaviour of disruption generated runaways in JET

The disruption rate (the percentage of discharges that disrupt) in JET was found to drop steadily over the years. Recent campaigns (2005–2007) show a yearly averaged disruption rate of only 6% while from 1991 to 1995 this was often higher than 20%. Besides the disruption rate, the so-called disruptivity, or the likelihood of a disruption depending on the plasma parameters, has been determined. The disruptivity of plasmas was found to be significantly higher close to the three main operational boundaries for tokamaks; the low-q, high density and β-limit. The frequency at which JET operated close to the density-limit increased six fold over the last decade; however, only a small reduction in disruptivity was found. Similarly the disruptivity close to the low-q and β-limit was found to be unchanged. The most significant reduction in disruptivity was found far from the operational boundaries, leading to the conclusion that the improved disruption rate is due to a better technical capability of operating JET, instead of safer operations close to the physics limits. The statistics showed that a simple protection system was able to mitigate the forces of a large fraction of disruptions, although it has proved to be at present more difficult to ameliorate the heat flux.

https://iopscience.iop.org/article/10.1088/0029-5515/49/5/055011/pdf

Statistical analysis of disruptions in JET

Disruptions remain one of the most hazardous events in the operation of a tokamak device, since they can cause damage to the vacuum vessel and surrounding structures. Their potential danger increases with the plasma volume and energy content and therefore they will constitute an even more serious issue for the next generation of machines. For these reasons, in the recent years a lot of attention has been devoted to devise predictors, capable of foreseeing the imminence of a disruption sufficiently in advance, to allow time for undertaking remedial actions. In this paper, the results of applying fuzzy logic and classification and regression trees (CART) to the problem of predicting disruptions at JET are reported. The conceptual tools of fuzzy logic, in addition to being well suited to accommodate the opinion of experts even if not formulated in mathematical but linguistic terms, are also fully transparent, since their governing rules are human defined. They can therefore help not only in forecasting disruptions but also in studying their behaviour. The analysis leading to the rules of the fuzzy predictor has been complemented with a systematic investigation of the correlation between the various experimental signals and the imminence of a disruption. This has been performed with an exhaustive, non-linear and unbiased method based on decision trees. This investigation has confirmed that the relative importance of various signals can change significantly depending on the plasma conditions. On the basis of the results provided by CART on the information content of the various quantities, the prototype of an adaptive fuzzy logic predictor was trained and tested on JET database. Its performance is significantly better than the previous static one, proving that more flexible prediction strategies, not uniform over the whole discharge but tuned to the operational region of the plasma at any given time, can be very competitive and should be investigated systematically.

https://iopscience.iop.org/article/10.1088/0029-5515/48/3/035010/pdf

M.F. Johnson

Papers

Survey of disruption causes at JET

An advanced disruption predictor for JET tested in a simulated real-time environment

Behaviour of disruption generated runaways in JET

Statistical analysis of disruptions in JET

Prototype of an adaptive disruption predictor for JET based on fuzzy logic and regression trees