Data-driven local operator finding for reduced-order modelling of plasma systems: I. Concept and verifications

Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive. The demand for such models has surged in the past decade due to their potential to facilitate scientific research and expedite the development of plasma technologies. In line with the advancements in computational power and data-driven methods, we introduce the "Phi Method" in this two-part article. Part I presents this novel algorithm, which employs constrained regression on a candidate term library informed by numerical discretization schemes to discover discretized systems of differential equations. We demonstrate Phi Method's efficacy in deriving reliable and robust reduced-order models (ROMs) for three test cases: the Lorenz attractor, flow past a cylinder, and a 1D Hall-thruster-representative plasma. Part II will delve into the method's application for parametric dynamics discovery. Our results show that ROMs derived from the Phi Method provide remarkably accurate predictions of systems' behavior, whether derived from steady-state or transient-state data. This underscores the method's potential for transforming plasma system modeling.