# Dynamic Mode Decomposition for Plasma Diagnostics and Validation

## TL;DR

This paper applies Dynamic Mode Decomposition to analyze and model nonlinear plasma dynamics, enabling efficient data-driven predictions and interpretation of dominant modes in magnetohydrodynamics.

## Contribution

It introduces the use of DMD for plasma diagnostics, providing low-rank models that accurately reconstruct and predict plasma behavior from sparse data.

## Key findings

- DMD successfully characterizes plasma modes including spheromak and injector-driven modes
- The 3-mode DMD model achieves high-fidelity dynamic reconstructions
- DMD reduces computational costs while maintaining accuracy

## Abstract

We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix decomposition that correlates spatial features of computational or experimental data while simultaneously associating the spatial activity with periodic temporal behavior. DMD can produce low-rank, reduced order surrogate models that can be used to reconstruct the state of the system and produce high-fidelity future state predictions. This allows for a reduction in the computational cost, and, at the same time, accurate approximations of the problem, even if the data are sparsely sampled. We demonstrate the use of the method on both numerical and experimental data, showing that it is a successful mathematical architecture for characterizing the HIT-IS magnetohydrodynamics. Importantly, the DMD decomposition produces interpretable, dominant mode structures, including the spheromak mode and a pair of injector-driven modes. In combination, the 3-mode DMD model produces excellent dynamic reconstructions that can be used for future state prediction and/or control strategies.