Solar Activity Forecasting Using a Hybrid Conv1D-LSTM Model Validated on Solar Cycle 25

We present a hybrid Conv1D–Long Short-Term Memory (Conv1D-LSTM) deep-learning model for monthly sunspot number (SSN) forecasting, implemented in the Julia programming language using Flux.jl. The model is trained on the complete Sunspot Index and Long-term Solar Observations (SILSO) dataset (January 1749–February 2026; 3326 months) with a physically motivated partition aligned with solar cycle boundaries: training on Cycles 1 – 23, validation on Cycle 24, and test on Cycle 25. The input window size ( $W = 60$ W = 60 months) is determined objectively from the autocorrelation structure of the training series, a value that corresponds physically to approximately half the Schwabe cycle and captures the phase memory necessary for short-term solar activity prediction. Morphological similarity between Cycle 25 and historical cycles is quantified via Dynamic Time Warping (DTW), providing independent astrophysical context for the forecast. Model robustness is assessed through rolling walk-forward cross-validation over Cycles 20 – 23 (mean absolute error (MAE) = 17.90 ± 2.11 17.90 ± 2.11 SSN (sunspot number) units, mean over four folds). Using a one-step-ahead evaluation protocol (in which each prediction uses the 60 preceding real observations as input, consistent with operational space weather forecasting), the model achieves MAE = 10.17 and root mean square error (RMSE) = 14.89 on Cycle 24, and MAE = 13.92 and RMSE = 19.24 on Cycle 25. A retrospective evaluation against the confirmed Cycle 25 maximum (SSN ≈ 160.9, October 2024) yields an amplitude error of 4.0%, compared with a 28.5% underestimate by the NOAA/NASA consensus panel. We note that this comparison is made with the observational advantage of hindsight: the confirmed maximum falls within our test set, whereas prior studies necessarily operated under prospective uncertainty. While the 4.0% error reflects excellent monthly tracking fidelity, this is distinct from the more challenging task of predicting cycle amplitude 5+ years in advance: the one-step-ahead protocol relies on the 60 preceding real observations as input and should not be interpreted as evidence of prospective long-range forecasting skill. The complete, reproducible Julia source code is publicly available at https://github.com/hernandguerreroc/solar-forecast-julia .