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Many scientific problems can be formulated as sparse regression, i.e., regression onto a set of parameters when there is a desire or expectation that some of the parameters are exactly zero or do not substantially contribute. This includes many problems in signal and image processing, system identification, optimization, and parameter estimation methods such as Gaussian process regression. Sparsity facilitates exploring high-dimensional spaces while finding parsimonious and interpretable solutions. In the present work, we illustrate some of the important ways in which sparse regression appears in plasma physics and point out recent contributions and remaining challenges to solving these problems in this field. A brief review is provided for the optimization problem and the state-of-the-art solvers, especially for constrained and high-dimensional sparse regression. 

Abstract Alfvén eigenmodes (AEs) are an important and complex class of plasma dynamics commonly observed in tokamaks and other plasma devices. In this work, we manually labeled a small database of 26 discharges from the DIII-D tokamak in order to train simple neural-network-based models for classifying AEs. The models provide spatiotemporally local identification of four types of AEs by using an array of 40 electron cyclotron emission (ECE) signals as inputs. Despite the minimal dataset, this strategy performs well at spatiotemporally localized classification of AEs, indicating future opportunities for more sophisticated models and incorporation into real-time control strategies. The trained model is then used to generate spatiotemporally-resolved labels for each of the 40 ECE measurements on a much larger database of 1112 DIII-D discharges. This large set of precision labels can be used in future studies for advanced deep predictors and new physical insights.