Dynamic Mode Decomposition for data-driven analysis and reduced-order
  modelling of ExB plasmas: I. Extraction of spatiotemporally coherent patterns
Farbod Faraji Maryam Reza Aaron Knoll J. Nathan Kutz
In this two-part article, we evaluate the utility and the generalizability of
the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and
reduced-order modelling of plasma dynamics in cross-field ExB configurations.
The DMD algorithm is an interpretable data-driven method that finds a best-fit
linear model describing the time evolution of spatiotemporally coherent
structures (patterns) in data. We have applied the DMD to extensive
high-fidelity datasets generated using a particle-in-cell (PIC) code based on a
cost-efficient reduced-order PIC scheme. In this part, we first provide an
overview of the concept of DMD and its underpinning Proper Orthogonal and
Singular Value Decomposition methods. Two of the main DMD variants are next
introduced. We then present and discuss the results of the DMD application in
terms of the identification and extraction of the dominant spatiotemporal modes
from high-fidelity data over a range of simulation conditions. We demonstrate
that the DMD variant based on variable projection optimization (OPT-DMD)
outperforms the basic DMD method in identification of the modes underlying the
data, leading to notably more reliable reconstruction of the ground-truth.
Furthermore, we show in multiple test cases that the discrete frequency
spectrum of OPT-DMD-extracted modes is consistent with the temporal spectrum
from the Fast Fourier Transform of the data. This observation implies that the
OPT-DMD augments the conventional spectral analyses by being able to uniquely
reveal the spatial structure of the dominant modes in the frequency spectra,
thus, yielding more accessible, comprehensive information on the spatiotemporal
characteristics of the plasma phenomena.