Data-driven local operator finding for reduced-order modelling of plasma
  systems: II. Application to parametric dynamics
Farbod Faraji Maryam Reza Aaron Knoll J. Nathan Kutz
Real-world systems often exhibit dynamics influenced by various parameters,
either inherent or externally controllable, necessitating models capable of
reliably capturing these parametric behaviors. Plasma technologies exemplify
such systems. For example, phenomena governing global dynamics in Hall
thrusters (a spacecraft propulsion technology) vary with various parameters,
such as the "self-sustained electric field". In this Part II, following on the
introduction of our novel data-driven local operator finding algorithm, Phi
Method, in Part I, we showcase the method's effectiveness in learning
parametric dynamics to predict system behavior across unseen parameter spaces.
We present two adaptations: the "parametric Phi Method" and the "ensemble Phi
Method", which are demonstrated through 2D fluid-flow-past-a-cylinder and 1D
Hall-thruster-plasma-discharge problems. Comparative evaluation against
parametric OPT-DMD in the fluid case demonstrates superior predictive
performance of the parametric Phi Method. Across both test cases, parametric
and ensemble Phi Method reliably recover governing parametric PDEs and offer
accurate predictions over test parameters. Ensemble ROM analysis underscores
Phi Method's robust learning of dominant dynamic coefficients with high
confidence.