Sunspot Activity Prediction Model Based on Cycle Similarity and Echo State Network

This paper aims to develop models based on historical observational data to enhance the prediction of sunspots in future phases. Initially, we collected public data on solar cycles. We applied the tvWSE algorithm for waveform decomposition of the time series, yielding multi-time scale results for trend, periodic, and chaotic components. Leveraging the predictability of the periodic component, we selected the Sunspot Number and the flux of radio waves in the 10.7 cm band as key feature parameters. Based on the Hurst index, we retained only the periodic component to reconstruct the time series waveform. We used the Echo State Network for shortterm forecasting of the SSN and F10.7 values' smoothed monthly averages. Through prediction, we further employed Ridge Regression to establish an approximate linear relationship between each solar cycle and the SSN and F10.7 values, predicting that Cycle 26 will start in March 2031 and end in November 2041. Then, we intuitively performed longterm forecasting using a heliophysical model based on “similar cycles” of solar activity to predict the start time and duration of the next solar maximum. After analyzing the Spearman correlation of various feature parameters, we selected the maximum, minimum, and duration of solar cycles to construct a composite similarity index and identify similar cycles for the start and duration periods. After comparing the characteristic variables of Cycle 26's prediction with other cycles, we found identical cycles around the start period T 1 as Cycles <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$13,16,20$</tex>, and 23 and around <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T 2$</tex> as Cycles <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$7,13,15$</tex>, and 16. Consequently, we predict the start time and duration of the maximum of Cycle 26 to be between February and July 2033 and between 15.472 and 22.988 months, respectively. Finally, we employed the PSO algorithm to fine-tune the ESN prediction model, further predicting the nonlinear components of sunspot numbers and areas' smoothed monthly averages. The forecasts indicate that the total monthly sunspot numbers for Cycles 25 and 26 are approximately 5440 and 6529, with entire sunspot areas of 54780 and 61260, respectively.