Forecast of Solar Cycle 25 based on Hybrid CNN-Bidirectional-GRU (CNN-BiGRU) model and Novel Gradient Residual Correction (GRC) Technique

In this study, a hybrid deep-learning(DL) model is proposed, which consists of a Convolution-Neural-Network (CNN) and Bidirectional-Gated-Recurrent-Unit (Bi-GRU) for the prediction of sunspot numbers(SSN) of different frequencies along with novel post-processing techniques of Gradient-Residual-Correction (GRC) to enhance the accuracy of the predictions further. GRC is utilized to reduce the residual present in the forecasted values. The AdaBoost regression model is implemented over the residual obtained from the prediction of training data using a hybrid CNN-BiGRU model with respect to the gradient of the training data points to predict the residual for the test data points. Ultimately, the predicted residual for test data points is summed up with the predicted test data points to achieve the final predictions. The results obtained from the proposed methods are compared with the results obtained from traditional DL models. The validation of the proposed method is carried out based on four performance metrics, namely Root Mean Squared Error(RMSE), Mean Absolute Scaled Error(MASE), Mean Absolute Error(MAE), and Mean Absolute Percentage Error(MAPE). A significant percentage of improvement is observed while using the GRC technique in comparison to all other experimented models for all four variants of SSN data. A maximum improvement of 85.71% has been achieved in comparison to the BiLSTM model over the 13-month smoothed SSN dataset on the basis of MAPE. Friedman Ranking is also performed as a non-parametric statistical test over the results of the performance measures. This model has been utilized for the forecast of solar cycle 25(SC25) over the annual mean of total SSN. It has been observed that the SC25 is expected to reach its peak in the year 2024 with an annual average peak value of 143.641. Comparative analysis of SC25 and the peak of SSN in the ongoing cycle with the previous works are also carried out.