  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.
