Hybrid-Ensemble Deep-Learning Models to Enhance the Sunspot Prediction and Forecasting of Solar Cycle 26

This study comprehensively evaluates deep-learning models across three types of sunspot data: 13-month smoothed Sunspot Number (SSN), yearly SSN, and mean monthly SSN data. Traditional models such as LSTM, GRU, CNN, RNN, and BiLSTM are compared against proposed hybrid models: Hybrid1 (CNN-DilatedLSTM-BiLSTM-GRU), Hybrid2 (CNN-GRU-RNN with Dropout Regularization), Hybrid3 (CNN-GRU), Hybrid4 (CNN-GRU-RNN without Dropout) (Hybrid2 and Hybrid4 both integrate CNN-GRU-RNN architectures, but Hybrid2 introduces Dropout layers to reduce overfitting, making it a regularized version of Hybrid4), and a Hybrid Ensemble model (Hybrid2 + Hybrid4). Key metrics like RMSE, MAE, MSE, and R² are used to assess model performance. The results indicate that hybrid models consistently outperform traditional models across all datasets. Specifically, the Hybrid Ensemble achieves enhanced predictive accuracy, recording an RMSE of 4.062 and R² of 0.9964 for 13-month smoothed SSN data, an RMSE of 22.11 and R² of 0.8920 for yearly SSN data, and an RMSE of 24.61 and R² of 0.8826 for mean monthly SSN data. These findings demonstrate the ability of hybrid models, especially the Hybrid Ensemble, to effectively capture complex patterns in sunspot time-series data.

In addition to model evaluation, this study provides forecasted SSN values for Solar Cycle 26, projecting a gradual increase in solar activity from 2025 (SSN: 112.39) to a peak in 2036 (SSN: 165.35), followed by a slight decline in 2037 (SSN: 155.25), with the lowest SSN occurring in 2032 (SSN: 10.41). These forecasts align well with known solar cycle variations and offer valuable insights into upcoming solar activity and its implications for space weather, climate, and technology. A Friedman non-parametric test was conducted to rank model performance, confirming the Hybrid Ensemble as the top performer. Holm-adjusted multiple comparisons showed negligible differences, reinforcing the robustness of the hybrid and ensemble approaches. This research highlights the value of combining different architectures to improve forecasting accuracy, especially for complex scientific time-series data such as solar activity.