Dynamic Mode Decomposition for data-driven analysis and reduced-order
  modelling of ExB plasmas: II. dynamics forecasting
Farbod Faraji Maryam Reza Aaron Knoll J. Nathan Kutz
In part I of the article, we demonstrated that a variant of the Dynamic Mode
Decomposition (DMD) algorithm based on variable projection optimization, called
Optimized DMD (OPT-DMD), enables a robust identification of the dominant
spatiotemporally coherent modes underlying the data across various test cases
representing different physical parameters in an ExB simulation configuration.
As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs)
by construction, in this paper, we extend the application of the OPT-DMD and
investigate the capabilities of the linear ROM from this algorithm toward
forecasting in time of the plasma dynamics in configurations representative of
the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and
over a range of simulation parameters in each test case. The predictive
capacity of the OPT-DMD ROM is assessed primarily in terms of short-term
dynamics forecast or, in other words, for large ratios of training-to-test
data. However, the utility of the ROM for long-term dynamics forecasting is
also presented for an example case in the radial-azimuthal configuration. The
model's predictive performance is heterogeneous across various test cases.
Nonetheless, a remarkable predictiveness is observed in the test cases that do
not exhibit highly transient behaviors. Moreover, in all investigated cases,
the error between the ground-truth and the reconstructed data from the OPT-DMD
ROM remains bounded over time within both the training and the test window. As
a result, despite its limitation in terms of generalized applicability to all
plasma conditions, the OPT-DMD is proven as a reliable method to develop low
computational cost and highly predictive data-driven reduced-order models in
systems with a quasi-periodic global evolution of the plasma state.