Special Issue: Machine Learning Methods in Plasma Physics

In recent years, research in plasma physics has made significant progress. One area of focus is the advancement of techniques for analyzing the ever-increasing amounts of data generated from experiments and simulations. This has led to the flourishing of novel machine learning and uncertainty quantification methods. Another direction of research is to enhance artificial-intelligence and machine-learning algorithms themselves by integrating knowledge about the studied systems into the inference process. This approach leads to the development of physics-informed algorithms, which take into account constraints such as energy or momentum conservation.

As machine learning and data-driven techniques continue to gain momentum in plasma physics research, we have compiled a collection of papers from authors who are actively involved in these areas. This special issue covers a wide range of topics, including physics-informed machine learning, reduced-complexity approaches, experimental design, and real-time control applications. In the following paragraphs, we provide a summary of each paper included in this issue.

The progress in the application of data-driven algorithms is largely driven by the increasing availability of training data. Accordingly, several papers in this special issue address the challenges of improved data generation, data augmentation, and data selection. Dave et al.[1] utilize generative adversial networks to synthesize time-series such as the plasma current, which can be used to train other algorithms. In the paper of Rath et al.,[2] time-series data augmentation is explored with a focus on the robust handling of outlying data points, leading to the use of Student-t processes instead of the more familiar Gaussian processes based on experimental data.

Interpolating machine-learning algorithms, such as Gaussian processes, often suffer from a super-linear run-time dependency on the amount of data. To address this challenge, Kremers et al.[3] propose a data thinning approach based on a two-step clustering that reduces the amount of redundant data. This allows for the removal of data points that have limited impact on the quality of the resulting model, reducing both computational costs and model complexity. Gaffney et al.[4] propose a different approach for collecting simulation data using ideas from active learning[5] and experimental design approaches.[6] They suggest generating simulation data primarily in information-rich regions.

In the field of artificial-intelligence and machine-learning algorithms, one recurring topic is the replacement of expensive simulator codes that encode the underlying physics processes with suitable emulators. These are algorithms that emulate the input–output relation of the simulator with significantly reduced computational effort. Depending on the application, emulators may be realized using neural networks, polynomial chaos expansions, or reduced complexity models. Emulators are often used to perform sensitivity studies or inferences that are otherwise numerically challenging using the underlying simulator. The paper of Köberl et al.[7] demonstrates such an application, analyzing the uncertainty of a 3D magnetohydrodynamic equilibrium reconstruction using an emulator based on polynomial chaos expansions. While other machine-learning methodologies are useful, neural networks are the most common emulators due to the availability of open-source libraries and generic applicability. In Honda et al.,[8] a convolutional neural network emulates gyrokinetic simulations and shows some promising generalization capabilities in predicting the heat fluxes of ions and electrons. Similarly, in Narita et al,[9] a neural network is used to compute diffusive and non-diffusive transport parameters of tokamak fusion plasmas. Cheng et al.[10] compare different machine-learning algorithms for predicting properties of helicon plasmas and conclude that their deep neural networks outperform other approaches.

Neural networks have very fast response times, which opens up the possibility of using them for real-time control or online monitoring diagnostic settings. Tang et al.[11] describe the implementation of a recurrent neural network as a disruption predictor into a control system intended to gracefully shut down the device before a damaging disruption can occur. Similarly, Morosohk et al.[12] describe an application of neural networks, using Thomson scattering diagnostic data for real-time profile reconstruction, allowing for improved machine control based on derived physics information.

The recent trend in machine learning, which incorporates physics knowledge, is reflected in the papers of T. Nishizawa[13] and T. M. Tyranowski et al.[14] In the former paper, transport parameters are inferred based on an integrated data analysis approach, using an appropriately constrained Gaussian process. In the latter paper, a reduced complexity model for the kinetic Vlasov equation is derived, taking the underlying Hamiltonian structure of the Vlasov equation into account. This model significantly improves upon standard approaches like dynamic mode decomposition or singular value decomposition.

The intersection between plasma physics research and data science is anticipated to become increasingly interconnected in the future. As such, it is our hope that this compilation of papers will serve as a valuable source of inspiration for future endeavors in this field.