Genetic Algorithm for Inferring Model Parameters for Flux Transport Dynamo Simulation

TL;DR

This work tackles the challenge of inferring time-varying internal solar dynamo parameters from solar-cycle observations by coupling a mean-field flux-transport dynamo model with a genetic algorithm. The parameters $u_0(t)$ and $s_0(t)$ are encoded as sine-series coefficients up to $l_{\max}=4$ and optimized to maximize a Sunspot Number-based fitness, $F=\alpha r_{\mathrm{sunspot}}-(1-\alpha)e_{\mathrm{sunspot}}$, with $SSN=\gamma B_\phi^2(r=0.7R_\odot,\theta=15^\circ)$ and $\alpha=0.9$. Validation on simulation data yields high SSN fidelity (e.g., $r=0.975$ in Step 1, $r=0.995$ in Step 2) and reduced parameter errors, while application to historical SSN (1723–2024) reveals plausible cycle-to-cycle variability in $u_0$ and $s_0$, with Dalton Minimum signatures and memory between poloidal and toroidal field generation. The approach offers a data-driven pathway to reconstruct past solar interior dynamics and can be extended to isotope-based SSN records, enhancing our understanding of long-term solar activity evolution.

Abstract

The Sun exhibits an 11-year cyclic variation, maintained by dynamo action in the solar interior. Mean-field flux transport dynamo models have successfully reproduced most of the features observed in solar cycles, while the model includes many free parameters, such as the speed of the meridional flow and the amplitude of the poloidal field generation. Inferring these free parameters is on demand because they correspond to the solar interior condition. We suggest a novel method for inferring the free parameters using a genetic algorithm. At each generation, we evaluate the fitness of our simulation against the observational data and optimize the parameters. We apply our method to the observed solar cycle data from 1723 to 2024 and successfully reproduce the observations from both qualitative and quantitative perspectives. We expect our method to be applicable to sunspot numbers, even those obtained from isotope data and historical documents, in the future, to better understand past solar interior dynamics.

Figures (6)

• Figure 1: Overview of our Genetic Algorithms. Panel(a) represents $n$-th generation. The black filled circles indicate individuals. Panel (b) represents the Genetic Algorithms operations. After two individuals are selected, crossover and mutation are performed with $80\%$ and $30\%$ probability, respectively. We repeat these operations until 30 individuals are created. Panel(c) represents the $n+1$-th generation. By repeating (a) to (c), leads to the optimal solution.
• Figure 2: Evolution of the toroidal and poloidal magnetic field components. Panels a, b, c, and d are results separated by intervals of 3.83 years. In panels a-d, the red and blue colors represent the toroidal magnetic field $B_\phi$, and the contour lines are magnetic field lines of the poloidal field. The solid and dashed lines indicate clockwise and counterclockwise field. These results are characterized by a cycle period of $22.028~\mathrm{yr}$. Panel e shows a butterfly diagram for 58.2 years. The color contours represent $B_r$ at the top boundary ($r=R_\odot$), and the contour lines represent $B_\phi$ around the base of the convection zone $r=0.7R_\odot$.
• Figure 3: Comparison between the ground truth data generated by the simulation and our inference. Panels a, c, and e (Step 1) show the results of inferring only the time variation of $u_0$, and panels b, d, and f show the results of inferring the time variation of $s_0$ with $u_0$ obtained in Step 1. Panels a and b show the time variation of SSN. Panels c and d show the time variation of $u_0$, and panels e and f show the time variation of $s_0$. The red and blue colors show the ground truth and our GA inference, respectively.
• Figure 4: Inference result for the observational data. Panel a shows the time variation of SSN. The red and blue represent the observational data and GA inference, respectively. The observed SSN is yearly mean total sunspot number by SILSO (Sunspot Number Version 2.0 silso_smoothed_ssn. We interpolate the data to achieve 40-day intervals for the inference. Inference is performed every $5$ cycles, and we merge all the inferences into a plot. Panels b and c represent the time variations of the inferred $u_0$ and $s_0$, respectively.
• Figure 5: Relation between $s_0$ and sunspot numbers. Panel a shows a scatter plot of the peak value of $s_0$ at the $n$-th cycle and the amplitude of the $n$-th sunspot number. Panel b shows a scatter plot of the peak value of $s_0$ at the $n$-th cycle and the amplitude of the $n+1$-th sunspot number. The correlation coefficients for the panels a and b are 0.763 and 0.916, indicating a time lag between the poloidal and toroidal field generations.