Data-driven reduced-order modelling of the plasma systems dynamics

Despite the increasing need for computationally efficient, predictive, and low-dimensional (low-order) plasma models, these have remained elusive so far. The crucial need for such models stems, in part, from the breakthroughs they can enable in scientific research into yet-unresolved plasma phenomena. Furthermore, these models can boost the efforts toward realizing fusion energy and can revamp the development of advanced plasma-based technologies. Machine-learning (ML) and data-driven (DD) methods can play a transformative role toward achieving predictive, generalizable, and interpretable reduced-order models (ROMs) for plasma systems. Motivated by the above, the overarching objective of this thesis is to explore the landscape of ML/DD techniques for physics modelling and to examine a subset of approaches among those with the highest promise to realize predictive plasma ROMs. Toward this goal, a critical literature review is performed. Accordingly, two categories of DD algorithms are down-selected. The algorithms in the first category learn and predict the time evolution of global structures (modes) underlying the data. From this category, the Optimized Dynamic Mode Decomposition (OPT-DMD) method is chosen. The second selected category comprises local dynamics discovery algorithms, where the methods discover the differential equations governing the dynamics. A novel method belonging to this category, termed “Phi Method”, is established and extensively assessed. The predictive performance of ROMs from OPT-DMD and Phi Method is evaluated across a wide array of test cases with varying dynamics complexity. Both approaches demonstrate remarkable potential for forecasting the plasma state. However, by the merit of its local dynamics learning, Phi Method presents a higher degree of flexibility for ROM development. Moreover, the Phi Method ROMs accurately discover parametric dependencies of the dynamics, a crucial aspect for any fully generalizable plasma model. To conclude, the next advancement steps on Phi Method and some promising future research directions in ML-enabled plasma modelling are outlined.