Parametric Dynamic Mode Decomposition for Nuclear Fusion: Applications to Magnetohydrodynamics

Magnetohydrodynamics (MHD) investigates the dynamics of electrically conducting fluids interacting with magnetic fields. This theory is widely utilized for magnetic confinement fusion problems since both thermonuclear plasmas and some of the relevant operating fluids flowing in the blanket can be described as conducting fluids subjected to magnetic fields. The intrinsically multiphysical nature of MHD problems leads to complex and computationally expensive models, making them unsuited for multiquery applications such as parameter optimization and sensitivity analysis, as well as for online monitoring and control. Reduced-order modeling (ROM) offers a promising path to reduce computational costs while preserving accuracy; however, its application for MHD problems is still in its preliminary stages. This study continues the investigation started by the authors on ROM techniques for MHD problems by considering a parametric version of the dynamic mode decomposition (DMD), aiming to retrieve a general linear representation of the parametric time-series MHD data. In particular, a Kalman filter (KF)-enhanced version of the technique is tested on a lead-lithium MHD flow subjected to a magnetic field of various intensities. The integration of KF in the reduced model approach aims at improving the accuracy of the reduced model by corrections based on data assimilated from sensors inside the geometry. Results demonstrate the reduced model potential to significantly reduce computational effort while maintaining acceptable accuracy, especially if coupled with the KF, making it suitable for fusion-relevant MHD applications.