Machine Learning and Deep Learning applications for the protection of nuclear fusion devices

This Thesis addresses the use of artificial intelligence methods for the protection of nuclear fusion devices with reference to the Joint European Torus (JET) Tokamak and the Wendenstein 7-X (W7-X) Stellarator. JET is currently the world's largest operational Tokamak and the only one operated with the Deuterium-Tritium fuel, while W7-X is the world's largest and most advanced Stellarator. For the work on JET, research focused on the prediction of “disruptions”, and sudden terminations of plasma confinement. For the development and testing of machine learning classifiers, a total of 198 disrupted discharges and 219 regularly terminated discharges from JET. Convolutional Neural Networks (CNNs) were proposed to extract the spatiotemporal characteristics from plasma temperature, density and radiation profiles. Since the CNN is a supervised algorithm, it is necessary to explicitly assign a label to the time windows of the dataset during training. All segments belonging to regularly terminated discharges were labelled as 'stable'. For each disrupted discharge, the labelling of 'unstable' was performed by automatically identifying the pre-disruption phase using an algorithm developed during the PhD. The CNN performance has been evaluated using disrupted and regularly terminated discharges from a decade of JET experimental campaigns, from 2011 to 2020, showing the robustness of the algorithm. Concerning W7-X, the research involved the real-time measurement of heat fluxes on plasma-facing components. THEODOR is a code currently used at W7-X for computing heat fluxes offline. However, for heat load control, fast heat flux estimation in real-time is required. Part of the PhD work was dedicated to refactoring and optimizing the THEODOR code, with the aim of speeding up calculation times and making it compatible with real-time use. In addition, a Physics Informed Neural Network (PINN) model was proposed to bring thermal flow computation to GPUs for real-time implementation

Physics-guided machine learning approaches to predict stability properties of fusion plasmas

Disruption prediction and avoidance is a critical need for next-step tokamaks such as the International Thermonuclear Experimental Reactor (ITER). The Disruption Event Characterization and Forecasting Code (DECAF) is a framework used to fully determine chains of events, such as magnetohydrodynamic (MHD) instabilities, that can lead to disruptions. In this thesis, several interpretable and physics-guided machine learning techniques (ML) to forecast the onset of resistive wall modes (RWM) in spherical tokamaks have been developed and incorporated into DECAF. The new DECAF model operates in a multi-step fashion by analysing the ideal stability properties and then by including kinetic effects on RWM stability. First, a random forest regressor (RFR) and a neural network (NN) ensemble are employed to reproduce the change in plasma potential energy without wall effects, δWno-wall, computed by the DCON ideal stability code for a large database of equilibria from the National Spherical Torus Experiment (NSTX). Moreover, outputs from the ML models are reduced and manipulated to get an estimation of the no-wall β limit, βno-wall, (where β is the ratio of plasma pressure to magnetic confinement field pressure). This exercise shows that the ML models are able to improve previous DECAF characterisation of stable and unstable equilibria and achieve accuracies within 85-88%, depending on the chosen level of interpretability. The physics guidance imposed on the NN objective function allowed for transferability outside the training domain by testing the algorithm on discharges from the Mega Ampere Spherical Tokamak (MAST). The estimated βno-wall and other important plasma characteristics, such as rotation, collisionality and low frequency MHD activity, are used as input to a customised random forest (RF) classifier to predict RWM stability for a set of human-labeled NSTX discharges. The proposed approach is real-time compatible and outperforms classical cost-sensitive methods by achieving a true positive rate (TPR) up to 90%, while also resulting in a threefold reduction in the training time. Finally, a model-agnostic method based on counterfactual explanations is developed in order to further understand the model's predictions. Good agreement is found between the model's decision and the rules imposed by physics expectation. These results also motivate the usage of counterfactuals to simulate real-time control by generating the βN levels that would keep the RWM stable

Data driven theory for knowledge discovery in the exact sciences with applications to thermonuclear fusion

In recent years, the techniques of the exact sciences have been applied to the analysis of increasingly complex and non-linear systems. The related uncertainties and the large amounts of data available have progressively shown the limits of the traditional hypothesis driven methods, based on first principle theories. Therefore, a new approach of data driven theory formulation has been developed. It is based on the manipulation of symbols with genetic computing and it is meant to complement traditional procedures, by exploring large datasets to find the most suitable mathematical models to interpret them. The paper reports on the vast amounts of numerical tests that have shown the potential of the new techniques to provide very useful insights in various studies, ranging from the formulation of scaling laws to the original identification of the most appropriate dimensionless variables to investigate a given system. The application to some of the most complex experiments in physics, in particular thermonuclear plasmas, has proved the capability of the methodology to address real problems, even highly nonlinear and practically important ones such as catastrophic instabilities. The proposed tools are therefore being increasingly used in various fields of science and they constitute a very good set of techniques to bridge the gap between experiments, traditional data analysis and theory formulation

Performance Comparison of Machine Learning Disruption Predictors at JET

Reliable disruption prediction (DP) and disruption mitigation systems are considered unavoidable during international thermonuclear experimental reactor (ITER) operations and in the view of the next fusion reactors such as the DEMOnstration Power Plant (DEMO) and China Fusion Engineering Test Reactor (CFETR). In the last two decades, a great number of DP systems have been developed using data-driven methods. The performance of the DP models has been improved over the years both for a more appropriate choice of diagnostics and input features and for the availability of increasingly powerful data-driven modelling techniques. However, a direct comparison among the proposals has not yet been conducted. Such a comparison is mandatory, at least for the same device, to learn lessons from all these efforts and finally choose the best set of diagnostic signals and the best modelling approach. A first effort towards this goal is made in this paper, where different DP models will be compared using the same performance indices and the same device. In particular, the performance of a conventional Multilayer Perceptron Neural Network (MLP-NN) model is compared with those of two more sophisticated models, based on Generative Topographic Mapping (GTM) and Convolutional Neural Networks (CNN), on the same real time diagnostic signals from several experiments at the JET tokamak. The most common performance indices have been used to compare the different DP models and the results are deeply discussed. The comparison confirms the soundness of all the investigated machine learning approaches and the chosen diagnostics, enables us to highlight the pros and cons of each model, and helps to consciously choose the approach that best matches with the plasma protection needs

Performance Comparison of Machine Learning Disruption Predictors at JET

Reliable disruption prediction (DP) and disruption mitigation systems are considered unavoidable during international thermonuclear experimental reactor (ITER) operations and in the view of the next fusion reactors such as the DEMOnstration Power Plant (DEMO) and China Fusion Engineering Test Reactor (CFETR). In the last two decades, a great number of DP systems have been developed using data-driven methods. The performance of the DP models has been improved over the years both for a more appropriate choice of diagnostics and input features and for the availability of increasingly powerful data-driven modelling techniques. However, a direct comparison among the proposals has not yet been conducted. Such a comparison is mandatory, at least for the same device, to learn lessons from all these efforts and finally choose the best set of diagnostic signals and the best modelling approach. A first effort towards this goal is made in this paper, where different DP models will be compared using the same performance indices and the same device. In particular, the performance of a conventional Multilayer Perceptron Neural Network (MLP-NN) model is compared with those of two more sophisticated models, based on Generative Topographic Mapping (GTM) and Convolutional Neural Networks (CNN), on the same real time diagnostic signals from several experiments at the JET tokamak. The most common performance indices have been used to compare the different DP models and the results are deeply discussed. The comparison confirms the soundness of all the investigated machine learning approaches and the chosen diagnostics, enables us to highlight the pros and cons of each model, and helps to consciously choose the approach that best matches with the plasma protection needs

2022 Review of Data-Driven Plasma Science

Data-driven science and technology offer transformative tools and methods to science. This review article highlights the latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS), i.e., plasma science whose progress is driven strongly by data and data analyses. Plasma is considered to be the most ubiquitous form of observable matter in the universe. Data associated with plasmas can, therefore, cover extremely large spatial and temporal scales, and often provide essential information for other scientific disciplines. Thanks to the latest technological developments, plasma experiments, observations, and computation now produce a large amount of data that can no longer be analyzed or interpreted manually. This trend now necessitates a highly sophisticated use of high-performance computers for data analyses, making artificial intelligence and machine learning vital components of DDPS. This article contains seven primary sections, in addition to the introduction and summary. Following an overview of fundamental data-driven science, five other sections cover widely studied topics of plasma science and technologies, i.e., basic plasma physics and laboratory experiments, magnetic confinement fusion, inertial confinement fusion and high-energy-density physics, space and astronomical plasmas, and plasma technologies for industrial and other applications. The final section before the summary discusses plasma-related databases that could significantly contribute to DDPS. Each primary section starts with a brief introduction to the topic, discusses the state-of-the-art developments in the use of data and/or data-scientific approaches, and presents the summary and outlook. Despite the recent impressive signs of progress, the DDPS is still in its infancy. This article attempts to offer a broad perspective on the development of this field and identify where further innovations are required

Calculation of the runaway electron current in tokamak disruptions

$\textit{Tokamak disruptions}$ can give rise to the $\textit{runaway phenomenon}$, which is typical in plasma physics and describes the almost unbound acceleration of electrons to relativistic velocities and can lead to the formation of a $\textit{runaway electron beam}$. In tokamak reactors like ITER, impacts of such a beam can damage the reactor wall, motivating the development of computationally efficient and accurate simulation methods for the runaway electron current. In present simulation software, the $\textit{reduced kinetic modeling}$ approach is used, which can be extended by using physically relevant moments of analytical runaway electron distribution functions. Because of this, calculation schemes for moments related to the density, the mean velocity and the mean kinetic energy of runaway electrons are deduced in this work and analysed with the help of ${\rm M{\small}{\small ATLAB}}$-implementations. At that, the screening effects of partially ionized impurities and different representations of the runaway electron generation region in momentum space are taken into account. First, numerical calculation rules for the primary $\textit{hot-tail}$ generation mechanism for isotropic and anisotropic two-dimensional descriptions of the runaway region are stated. They are then evaluated using the results of an ITER disruption simulation. After that, calculation concepts for said moments, related to the secondary $\textit{avalanche}$ generation mechanism, are derived. Different lower momentum boundaries for the runaway region and the influence of the partial screening of the nucleus by bound electrons are discussed on the basis of results calculated for different density combinations of a singly ionized deuterium-neon plasma. It is shown, that the analysed calculation schemes are physically valid and allow for the rapid investigation of physical quantities and parameter studies.Comment: master thesis with 189 pages, ${\rm M{\small}{\small ATLAB}}$-scripts available on reques