Sunspots are darkened regions on the Sun’s surface caused by intense magnetic disturbances and serve as crucial indicators of the solar cycle, which typically follows an approximately 11-year periodicity. These cycles have a profound influence on space weather, Earth’s climate, and the stability of modern technological systems, including satellite communications, GPS navigation, and power grid operations. The Sunspot Number (SSN) dataset, consisting of historical sunspot counts, represents a complex, nonlinear, and cyclic time series driven by solar magnetic activity. This study explores sunspot forecasting using advanced deep-learning architectures and large language model (LLM)-inspired approaches.
To improve prediction accuracy, three novel models are proposed: Hybrid H1 (CNN-BiLSTM-GRU), Hybrid H2 (CNN-GRU-RNN), and an Ensemble model that integrates both hybrid architectures with the Chronos framework. These models leverage convolutional layers for feature extraction, recurrent layers for temporal dependencies, attention mechanisms for enhanced focus on relevant patterns, and hyperparameter optimization to maximize performance across four SSN resolutions: daily, monthly mean, 13-month smoothed, and yearly data. Model performance is rigorously evaluated using RMSE, MAE, MSE, and (R^{2}) metrics, along with the Friedman ranking test and graphical analyses including line plots, scatter plots, box plots, and Taylor diagrams.
Experimental results demonstrate that all proposed models outperform traditional statistical methods and baseline deep learning and LLM-based models. For yearly SSN data, the Ensemble model shows the highest accuracy, with a 44% improvement over TimesFM and 27% over BiLSTM, while Hybrid H1 and H2 provide improvements of 41% and 42% over TimesFM, respectively. On the 13-month smoothed dataset, the Ensemble model improves forecasting by 47% over TimesFM and 15% over CNN, with Hybrid H1 and H2 yielding similar gains. For monthly mean data, the Ensemble model achieves an 18% improvement over TimeGPT and a remarkable 19% over LSTM. Daily data predictions show a 9.47% improvement for the Ensemble model over TimesFM and 21% over RNN, with Hybrid models following closely behind.
Using these best-performing models, long-term forecasts were extended on the yearly SSN dataset through the year 2110. The models predict peak sunspot activity in 2024, 2034, 2045, 2055, 2067, 2078, 2090, and 2102, corresponding to Solar Cycles 25 through 32. These predictions exhibit strong alignment with historical solar patterns, highlighting the reliability and advanced forecasting capacity of the proposed hybrid and ensemble deep-learning approaches, enriched by LLM-driven techniques, for modeling complex solar dynamics.
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