  Modeling and forecasting the solar wind-driven global magnetic field
perturbations is an open challenge. Current approaches depend on simulations of
computationally demanding models like the Magnetohydrodynamics (MHD) model or
sampling spatially and temporally through sparse ground-based stations
(SuperMAG). In this paper, we develop a Deep Learning model that forecasts in
Spherical Harmonics space 2, replacing reliance on MHD models and providing
global coverage at one minute cadence, improving over the current
state-of-the-art which relies on feature engineering. We evaluate the
performance in SuperMAG dataset (improved by 14.53%) and MHD simulations
(improved by 24.35%). Additionally, we evaluate the extrapolation performance
of the spherical harmonics reconstruction based on sparse ground-based stations
(SuperMAG), showing that spherical harmonics can reliably reconstruct the
global magnetic field as evaluated on MHD simulation.
