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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.

 

Intelligent mobile sensors, such as uninhabited aerial or underwater vehicles, are becoming prevalent in environmental sensing and monitoring applications. These active sensing platforms operate in unsteady fluid flows, including windy urban environments, hurricanes and ocean currents. Often constrained in their actuation capabilities, the dynamics of these mobile sensors depend strongly on the background flow, making their deployment and control particularly challenging. Therefore, efficient trajectory planning with partial knowledge about the background flow is essential for teams of mobile sensors to adaptively sense and monitor their environments. In this work, we investigate the use of finite-horizon model predictive control (MPC) for the energy-efficient trajectory planning of an active mobile sensor in an unsteady fluid flow field. We uncover connections between trajectories optimized over a finite-time horizon and finite-time Lyapunov exponents of the background flow, confirming that energy-efficient trajectories exploit invariant coherent structures in the flow. We demonstrate our findings on the unsteady double gyre vector field, which is a canonical model for chaotic mixing in the ocean. We present an exhaustive search through critical MPC parameters including the prediction horizon, maximum sensor actuation, and relative penalty on the accumulated state error and actuation effort. We find that even relatively short prediction horizons can often yield energy-efficient trajectories. We also explore these connections on a three-dimensional flow and ocean flow data from the Gulf of Mexico. These results are promising for the adaptive planning of energy-efficient trajectories for swarms of mobile sensors in distributed sensing and monitoring. 

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. 

Abstract Modern tokamaks have achieved significant fusion production, but further progress towards steady-state operation has been stymied by a host of kinetic and MHD instabilities. Control and identification of these instabilities is often complicated, warranting the application of data-driven methods to complement and improve physical understanding. In particular, Alfvén eigenmodes are a class of ubiquitous mixed kinetic and MHD instabilities that are important to identify and control because they can lead to loss of confinement and potential damage to the walls of a plasma device. In the present work, we use reservoir computing networks to classify Alfvén eigenmodes in a large labeled database of DIII-D discharges, covering a broad range of operational parameter space. Despite the large parameter space, we show excellent classification and prediction performance, with an average hit rate of 91% and false alarm ratio of 7%, indicating promise for future implementation with additional diagnostic data and consolidation into a real-time control strategy.