Solar Cycles: How Magnetic Swings Sway the Future express
Sunspots are traces of magnetic fields that emerge on the surface. They live their own lives: spots closer to the equator tilt more, while those farther away tilt less. These two effects, like two knobs on an old radio, control how much magnetic field reaches the Sun's poles and accumulates there for the next cycle.
Researchers trained a neural network to solve the equation of magnetic field transport across the solar surface, embedding physical laws into it. This approach allowed them to separate the influence of spot tilt from that of latitude. They found that with rapid mixing of magnetic fields, the tilt effect is suppressed more, while with powerful plasma flows, the latitude effect dominates.
The key finding: the ratio of contributions from these two effects varies smoothly with the efficiency of the solar dynamo. This refines previous approximate formulas and reduces data scatter. The neural network approach yielded smaller errors than the traditional one-dimensional model and more reliably recovered nonlinear trends.
Such understanding helps better predict the strength of future solar cycles, which affect satellites, communications, and even space missions.
Original abstract
as written by the authors arXiv:2602.16656
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 $$\Delta D_{\mathrm{LQ}}/\Delta D_{\mathrm{TQ}}$$ 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.
The solar cycle lasts about 11 years, but its strength can vary by factors: for example, the 24th cycle was nearly twice as weak as the previous one.