Data-driven local operator finding for reduced-order modelling of plasma systems: II. Application to parametric dynamics

TL;DR

This paper demonstrates a data-driven local operator finding algorithm, Phi Method, that effectively learns and predicts parametric plasma system dynamics, outperforming existing methods in accuracy and robustness across unseen parameters.

Contribution

The paper introduces the parametric and ensemble Phi Method adaptations, advancing data-driven reduced-order modeling for parametric plasma systems with superior predictive capabilities.

Findings

Outperforms parametric OPT-DMD in fluid flow prediction

Accurately recovers governing parametric PDEs

Provides robust learning of dynamic coefficients

Abstract

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.