Cluster, Classify, Regress: A General Method For Learning Discountinous Functions

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.Comment: 12 files,6 figure

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper, we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening up the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.This research was funded in part by the Ministerio de Economía, Industria y Competitividad of Spain, Grant No. ENE2015-68265. This research was carried out in part at the Max-Planck-Institute for Plasma Physics in Greifswald (Germany), whose hospitality is gratefully acknowledged. This research was supported in part by the U.S. Department of Energy, Office of Fusion Energy Sciences under Award DE-AC05-00OR22725. SIESTA runs have been carred out in Uranus, a supercomputer cluster located at Universidad Carlos III de Madrid and funded jointly by the European Regional Development Funds (EU-FEDER) Project No. UNC313-4E-2361, and by the Ministerio de Economía, Industria y Competitividad via the National Project Nos. ENE2009-12213-C03-03, ENE2012-33219, and ENE2012-31753

Forward modeling of collective Thomson scattering for Wendelstein 7-X plasmas: Electrostatic approximation

In this paper, we present a method for numerical computation of collective Thomson scattering (CTS). We developed a forward model, eCTS, in the electrostatic approximation and benchmarked it against a full electromagnetic model. Differences between the electrostatic and the electromagnetic models are discussed. The sensitivity of the results to the ion temperature and the plasma composition is demonstrated. We integrated the model into the Bayesian data analysis framework Minerva and used it for the analysis of noisy synthetic data sets produced by a full electromagnetic model. It is shown that eCTS can be used for the inference of the bulk ion temperature. The model has been used to infer the bulk ion temperature from the first CTS measurements on Wendelstein 7-X

Towards a new image processing system at Wendelstein 7-X: From spatial calibration to characterization of thermal events

Wendelstein 7-X (W7-X) is the most advanced fusion experiment in the stellarator line and is aimed at proving that the stellarator concept is suitable for a fusion reactor. One of the most important issues for fusion reactors is the monitoring of plasma facing components when exposed to very high heat loads, through the use of visible and infrared (IR) cameras. In this paper, a new image processing system for the analysis of the strike lines on the inboard limiters from the first W7-X experimental campaign is presented. This system builds a model of the IR cameras through the use of spatial calibration techniques, helping to characterize the strike lines by using the information given by real spatial coordinates of each pixel. The characterization of the strike lines is made in terms of position, size, and shape, after projecting the camera image in a 2D grid which tries to preserve the curvilinear surface distances between points. The description of the strike-line shape is made by means of the Fourier Descriptors