Data-Driven Forecasting of Solar and Geomagnetic Activity Using Relative Sunspot Numbers

Accurate modeling and forecasting of solar and geomagnetic activity is essential for advancing our fundamental understanding of solar-terrestrial interactions and magnetospheric dynamics. In this study, we propose a computational approach based on a Long Short-Term Memory (LSTM) neural network for predicting the 10.7 cm solar radio flux (\textnormal{F10.7}) and four widely used geomagnetic indices (\textit{K}\textsubscript{\textit{p}}, {\itshape Dst}, {\itshape ap}, and {\itshape AE}) using the Relative Sunspot Number (RSSN) as the primary input. To enhance the model's predictive capability, we introduce a physically motivated feature engineering strategy that incorporates nonlinear and temporal characteristics of solar dynamics, including quadratic and rolling-average features, as well as autoregressive information for each target variable. We employ a strictly leak-free Purged-Embargo validation strategy to prevent information leakage during model development. The framework is evaluated using hourly observations from 1 January 2000 to 10 January 2026, covering Solar Cycles 23, 24, and 25. Our proposed model achieves excellent predictive performance for the \textnormal{F10.7} and {\itshape Dst} indices, with coefficients of determination $R^2$ of 0.9639 and 0.9584, respectively. Good agreement is also obtained for the \textit{K}\textsubscript{\textit{p}} and {\itshape ap} indices ($R^2$ = 0.8642 and 0.8622), while the more dynamic {\itshape AE} index reaches an $R^2$ of 0.6939. These results demonstrate that the proposed framework provides an accurate and robust approach for forecasting solar and geomagnetic activity from a minimal set of input observations.