Learning physics-based reduced models from data for the
  Hasegawa-Wakatani equations
Constatin Gahr Ionut-Gabriel Farcas Frank Jenko
This paper focuses on the construction of non-intrusive Scientific Machine
Learning (SciML) Reduced-Order Models (ROMs) for nonlinear, chaotic plasma
turbulence simulations. In particular, we propose using Operator Inference
(OpInf) to build low-cost physics-based ROMs from data for such simulations. As
a representative example, we focus on the Hasegawa-Wakatani (HW) equations used
for modeling two-dimensional electrostatic drift-wave plasma turbulence. For a
comprehensive perspective of the potential of OpInf to construct accurate ROMs
for this model, we consider a setup for the HW equations that leads to the
formation of complex, nonlinear, and self-driven dynamics, and perform two sets
of experiments. We first use the data obtained via a direct numerical
simulation of the HW equations starting from a specific initial condition and
train OpInf ROMs for predictions beyond the training time horizon. In the
second, more challenging set of experiments, we train ROMs using the same
dataset as before but this time perform predictions for six other initial
conditions. Our results show that the OpInf ROMs capture the important features
of the turbulent dynamics and generalize to new and unseen initial conditions
while reducing the evaluation time of the high-fidelity model by up to five
orders of magnitude in single-core performance. In the broader context of
fusion research, this shows that non-intrusive SciML ROMs have the potential to
drastically accelerate numerical studies, which can ultimately enable tasks
such as the design and real-time control of optimized fusion devices.