An exploration of data-driven system identification and machine learning for plasma physics

Abstract

Plasma is the most common state of visible matter in the universe and provides a myriad of scientific and engineering applications. However, the complexity of these systems poses a significant challenge for understanding and controlling plasmas. Fortunately, machine learning is increasingly used to handle complex, nonlinear systems, and the field of machine learning is advancing at an unprecedented pace, propelled forward by advances in sensing technology and computing power. This thesis summarizes work towards applying modern machine learning algorithms for fluid and plasma physics applications, with a focus on the understanding and control of magnetohydrodynamic (MHD) phenomena and fusion-relevant plasmas. Although this work is primarily focused on machine learning, first conventional numerical techniques are used to implement a two-temperature Hall-MHD model into the 3D PSI-Tet code, followed by an investigation of the plasma dynamics in the HIT-SI experiment. These simulations agree well with experimental measurements, and indicate that low-densities are required for significant closed flux surfaces - a recommendation that is now helping to guide the next generation of experimental design. Next, plasma modeling with machine learning is discussed in the context of the hierarchy of plasma models and it is illustrated that there is "plenty of room at the bottom" for physics-constrained reduced order models that approximate more complex MHD or kinetic plasma models. Variants of the dynamic mode decomposition are explored on experimental data and simulations of the HIT-SI plasma device and indicate promise for magnetic mode spectroscopy and forecasting diagnostic measurements. Continuing, analytic reduced-order modeling methods are extended using techniques in system identification for extracting reduced-order models directly from data. In the process, new methods are invented to enforce physical constraints and stability in data-driven fluid and plasma models. For instance, the ability to build data-driven models that obey global conservation of energy or global conservation of cross-helicity is demonstrated, with promise for efficient simulations of ideal and resistive MHD turbulence. With the new functionality implemented into the open-source PySINDy code as part of this work, advanced system identification methods that can robustly extract dynamical equations from data are available to the larger scientific community.In total, this work illustrates that new machine learning methods can be directly tied with known physical laws in plasma physics, have promise to significantly impact much of the plasma physics and nonlinear systems fields, and can provide complementary, interpretable methods to the relatively black-box deep learning techniques that are frequently used in the plasma physics field for extracting diagnostic information, building reduced-order models, and performing real-time control.