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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.
Potential magnetic field solutions can be obtained based on the synoptic magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of the magnetogram is used to construct the current and divergence free magnetic field solution. This
Spherical Harmonics, $Y_ell^m(theta,phi)$, are derived and presented (in a Table) for half-odd-integer values of $ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the spherical-polar angles, $th
This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3,2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hil
The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how one can de
Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the existing