Forecasting solar cycles using the time-series dense encoder deep learning model

The solar cycle (SC), a phenomenon caused by the quasi-periodic regular activities in the Sun, occurs approximately every 11 years. Intense solar activity can disrupt the Earth’s ionosphere, affecting communication and navigation systems. Consequently, accurately predicting the intensity of the SC holds great significance, but predicting the SC involves a long-term time series, and many existing time series forecasting methods have fallen short in terms of accuracy and efficiency. The Time-series Dense Encoder model is a deep learning solution tailored for long time series prediction. Based on a multi-layer perceptron structure, it outperforms the best previously existing models in accuracy, while being efficiently trainable on general datasets. We propose a method based on this model for SC forecasting. Using a trained model, we predict the test set from SC 19 to SC 25 with an average mean absolute percentage error of 32.02, root mean square error of 30.3, mean absolute error of 23.32, and <italic>R</italic>² (coefficient of determination) of 0.76, outperforming other deep learning models in terms of accuracy and training efficiency on sunspot number datasets. Subsequently, we use it to predict the peaks of SC 25 and SC 26. For SC 25, the peak time has ended, but a stronger peak is predicted for SC 26, of 199.3, within a range of 170.8–221.9, projected to occur during April 2034.