Surface Flux Transport Modeling using Physics Informed Neural Networks

TL;DR

This paper introduces a Physics-Informed Neural Network model for simulating magnetic flux transport on the solar surface, offering improved accuracy and efficiency over traditional numerical methods, and aiding in understanding solar activity and predicting solar cycles.

Contribution

The paper presents a novel PINN-based model for solar magnetic flux transport, demonstrating its accuracy, efficiency, and ability to reproduce observed polar magnetic fields better than existing numerical schemes.

Findings

PINN model accurately reproduces observed polar magnetic fields

PINN approach is mesh-independent and computationally efficient

Model outperforms traditional Runge-Kutta schemes in flux conservation

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) modeling 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 (PINN)-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 PINN-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 PINN 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 PINN in solving advection-diffusion equations with a particular focus on heliophysics.