Applicability of Sunspot Number Prediction Across Multiple Timescales Based on Different MD-LSTM Frameworks

Abstract Forecasting sunspot number (SSN) is essential for understanding solar dynamics and mitigating space weather impacts. Previous studies have primarily focused on a single timescale or specific decomposition strategy, whereas the inherently complex and multi-scale nature of solar activity requires a unified predictive framework. In this study, four SSN series, including yearly mean (YMSSN), monthly mean (MMSSN), 13 month smoothed monthly (SMSSN), and daily (DSSN) total sunspot number, spanning from 1818 to 2024 were investigated. To address the multiple timescales SSN prediction challenges, a mode decomposition-long short-term memory (MD-LSTM) framework was proposed. Three MD methods, including empirical mode decomposition, ensemble empirical mode decomposition, and variational mode decomposition (VMD), were applied to decompose each series into intrinsic mode functions (IMFs). This decomposition mitigates non-stationarity effects, enabling clearer temporal pattern extraction. Subsequently, an LSTM network was used to capture long-term dependencies and nonlinearity within each IMF, thereby enhancing temporal modeling. Experiments consistently demonstrated that all MD-LSTM variants outperformed the baseline, confirming the advantage of incorporating decomposition. Among the hybrid frameworks, VMD-LSTM yielding more distinct components and superior performance, with R2 scores often above 0.99. Moreover, the consistent superiority was observed across all four timescales, supporting the applicability of the MD-LSTM framework. Finally, using optimal VMD-LSTM-SMSSN model, the ongoing solar cycle 25 was forecasted to peak at 158.57 in 2024 August, which aligns closely with recent observation. Furthermore, the model forecasts that solar cycle 26 will reach its maximum in 2035 February with a peak of 156.85, demonstrating the framework’s utility for long-term prediction.