Multiscale prediction of sunspot number using a wavelet-based hybrid deep learning model

The sunspot number (SSN) is one of the longest continuous quantitative records of solar activity and is widely used as a proxy for solar variability. Accurate SSN prediction is important for solar-cycle studies and space-weather applications, yet remains challenging owing to the quasi-periodic \(\sim\) 11-year solar cycle and the multiscale, nonlinear evolution of solar magnetic activity. In this study, we propose a multiscale hybrid model for predicting the 13-month smoothed SSN, using data from 1750–2025. A three-level discrete wavelet transform (DWT) decomposes the SSN series into one approximation component and three detail components, which are then modelled separately by an Inception-based convolutional neural network (InceptionCNN) and a bidirectional long short-term memory network (BiLSTM) before recombination. The one-step-ahead prediction experiment shows strong predictive performance on the test set, achieving an RMSE of 1.35, an MAE of 1.14, a MAPE of 2.36%, and an \(R^2\) of 0.9997. Moreover, recursive hindcast experiments indicate that using 12-month outputs for the approximation component ( cA -12 recursive model) can improve long-horizon recursive stability and reduce accumulated errors compared with the one-month recursive model. The 132-month forecast from the cA -12 recursive model suggests a solar minimum around April 2030, generally consistent with expectations for the ongoing Solar Cycle 25.