BOOK OF ABSTRACTS AND CONTRIBUTED PAPERS: International scientific conference Meeting on Operational and Research Capabilities for Better Understanding Solar-Terrestrial Interactions ,
Pages: 79-81,
https://doi.org/10.69646/aob250927
International scientific conference Meeting on Operational and Research Capabilities for Better Understanding Solar-Terrestrial Interactions
Published by: Scientific Society Isaac Newton

We apply the methods recent generalizations of the Physics -Informed Neural Networks (PINNs) , based on Kolmogorov -Arnold Networks and other interpolations, for the computation of magnetohydrodynamic (MHD) equilibria in the solar corona. Equilibrium curved -magnetic structures are an important topic in solar physics. They are described by solutions of the Grad –Shafranov (GS) equation, derived in the axisymmetric approximation. For example, the GS equation and its solutions are often used for magnetic -cloud reconstruction (e.g., to determine their geometries from observations, as studied by Isavnin et al. in 2011). GS -like solutions are also important for modelling the coronal mass ejection (CME) phenomenon, for which a simple force -free spheromak solution is used, as studied by Shiota & Kataoka in 2016 and Verbeke et al. in 2019. Hence, particular solutions of the GS equation, called Soloviev solutions , can also be implemented as time -dependent boundary conditions, as done by Linan et al. in 2023, which leads to a better, self -consistent CME evolution model. As another example, we consider the Lane –Emden (LE) equations, which are widely employed in astrophysics and relativistic mechanics. Our approach is general and may be exploited as an alternative to the standard PINN methodology as developed by Raissi et al. in 2019 and later.