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

arXiv: https://arxiv.org/abs/2403.01532 · HTML: https://mlsanity.com/paper/2403.01532/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 3 Mar 2024.

## Builds on (most cited first, 6 of 6)

- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: I. Extraction of spatiotemporally coherent patterns](https://mlsanity.com/paper/2308.13726/) (2023)
- [Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting](https://mlsanity.com/paper/2308.13727/) (2023)
- [Data-driven, multi-moment fluid modeling of Landau damping](https://mlsanity.com/paper/2209.04726/) (2022)
- [A comparison of Fourier and POD mode decomposition methods for high-speed Hall thruster video](https://mlsanity.com/paper/2205.14207/) (2022)

## Built on by (most cited first, 5 of 5)

- [Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics](https://mlsanity.com/paper/2405.11955/) (2024)
- [The Seismic Wavefield Common Task Framework](https://mlsanity.com/paper/2512.19927/) (2025)
- [Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspective](https://mlsanity.com/paper/2409.02349/) (2024)
- [A Comparison of Parametric Dynamic Mode Decomposition Algorithms for Thermal-Hydraulics Applications](https://mlsanity.com/paper/2503.24205/) (2025)
- [Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systems](https://mlsanity.com/paper/2410.16656/) (2024)

## Abstract (arXiv)

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.