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

arXiv: https://arxiv.org/abs/2403.01523 · HTML: https://mlsanity.com/paper/2403.01523/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 60 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)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Benchmarking sparse system identification with low-dimensional chaos](https://mlsanity.com/paper/2302.10787/) (2023)
- [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)

## 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)
- [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)
- [Multiscale autonomous forecasting of plasma systems' dynamics using neural networks](https://mlsanity.com/paper/2502.11203/) (2025)

## Abstract (arXiv)

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.