Data-driven reduced-order modeling of nonlinear MHD systems

Magnetized plasmas are highly complex, multi-scale systems and understanding their nonlinear dynamics traditionally requires high-resolution first-principles models which are numerically extensive. Fortunately, emerging data-driven techniques can be leveraged to develop interpretable reduced-order models of these highly nonlinear systems. The sparse identification of nonlinear dynamics (SINDy) algorithm [1] is one such method that identifies a minimal dynamical system model. In this work, we use projection-based model reduction [2] for an MHD system where energy and helicity are injected using time-invariant electric and magnetic fields on the top surface of a perfectly conducting cylinder, driving a saturated state that is sustained by periodic bursts of nonlinear dynamo activity. Then, we use the PySINDy package to build low-order sparse models to accurately describe the nonlinear dynamics of the system.

1 - S. Brunton et al., PNAS 113, 3932 (2016)

2 - A. Kaptanoglu et al., Phys. Rev. E 104, 015206 (2019)