Surface Flux Transport Modelling using Physics Informed Neural Networks

ABSTRACT Studying the magnetic field properties on the solar surface is crucial for understanding the solar and heliospheric activities, which in turn shape space weather in the solar system. Surface Flux Transport (SFT) modelling helps us to simulate and analyse the transport and evolution of magnetic flux on the solar surface, providing valuable insights into the mechanisms responsible for solar activity. In this work, we demonstrate the use of machine learning techniques in solving magnetic flux transport, making it accurate. We have developed a novel Physics-Informed Neural Networks (PINNs)-based model to study the evolution of Bipolar Magnetic Regions (BMRs) using SFT in one-dimensional azimuthally averaged and also in two-dimensions. We demonstrate the efficiency and computational feasibility of our PINNs-based model by comparing its performance and accuracy with that of a numerical model implemented using the Runge-Kutta Implicit-Explicit (RK-IMEX) scheme. The mesh-independent PINNs method can be used to reproduce the observed polar magnetic field with better flux conservation. This advancement is important for accurately reproducing observed polar magnetic fields, thereby providing insights into the strength of future solar cycles. This work paves the way for more efficient and accurate simulations of solar magnetic flux transport and showcases the applicability of PINNs in solving advection-diffusion equations with a particular focus on heliophysics. INTRODUCTION The dynamic processes on the solar surface exert a significant influence on the magnetic properties of the Sun. It is widely accepted that the generation of magnetic fields in the convection zone is the result of a dynamo mechanism (Petrovay 2000; Ossendrijver 2003; Nandy 2009; Choudhuri 2011, 2014; Charbonneau 2020). Solar active regions (AR) represent areas on the Sun's surface exhibiting intense magnetic activity. They often manifest as dark patches known as sunspots (Solanki 1993; Ruzmaikin 2001; Solanki 2003; Weiss 2006). These regions form as a result of strong toroidal flux tubes rising through the convection zone and emerging as Bipolar Magnetic Regions (BMRs) on the photosphere. Eventually, differential rotation comes into play and disrupts the poloidal field, giving rise to a toroidal field, and thereby the cycle continues (Fan 2009; Stein 2012; Cheung et al. 2016; Charbonneau 2020).