Investigating Nonlinear Quenching Effects on Polar Field Buildup in the Sun Using Physics-Informed Neural Networks

The solar dynamo relies on the regeneration of the poloidal magnetic field through processes strongly modulated by nonlinear feedbacks such as tilt quenching (TQ) and latitude quenching (LQ). These mechanisms play a decisive role in regulating the buildup of the Sun's polar field and, in turn, the amplitude of future solar cycles. In this work, we employ Physics-Informed Neural Networks (PINN) to solve the surface flux transport (SFT) equation, embedding physical constraints directly into the neural network framework. By systematically varying transport parameters, we isolate the relative contributions of TQ and LQ to polar dipole buildup. We use the residual dipole moment as a diagnostic for cycle-to-cycle amplification and show that TQ suppression strengthens with increasing diffusivity, while LQ dominates in advection-dominated regimes. The ratio $ΔD_{\mathrm{LQ}}/ΔD_{\mathrm{TQ}}$ exhibits a smooth inverse-square dependence on the dynamo effectivity range, refining previous empirical fits with improved accuracy and reduced scatter. The results further reveal that the need for a decay term is not essential for PINN set-up due to the training process. Compared with the traditional 1D SFT model, the PINN framework achieves significantly lower error metrics and more robust recovery of nonlinear trends. Our results suggest that the nonlinear interplay between LQ and TQ can naturally produce alternations between weak and strong cycles, providing a physical explanation for the observed even-odd cycle modulation. These findings demonstrate the potential of PINN as an accurate, efficient, and physically consistent tool for solar cycle prediction.

Surface Flux Transport Modelling using Physics Informed Neural Networks

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.