Application Of The Neural Network Method In Forecasting Of Solar Activity Indices

Solar activity directly or indirectly affects various physical phenomena on the Earth and causes space environment effects.Therefore,the research and prediction of solar activity has always attracted the attention of researchers in many fields.The sunspot number（SSN）and 10.7 cm solar radio flux(F_10.7)are two important parameters to measure the level of solar activity,and their accurate predictions have been valuable ingredients of both solar activity prediction and space weather prediction.Since these two indices are nonlinear and nonstationary time series,it would be more difficult to yield their accurate predictions based on ordinary statistical methods.Instead,this paper will try to use the Long Short-Term Memory（LSTM）,a neural network method based on nonlinear statistics,to predict these indices and evaluate the corresponding forecast effects.This work has not only research significance but also potential application values.In this paper,based on the training results of the LSTM model on the daily average value of F_10.7 from 1947 to 1995,the short-term（1-3 days in advance）forecast experiment of F_10.7 from 1996 to 2019 is carried out.The results show that the root mean square error is small（between 6.12 sfu and 6.25 sfu）,and the prediction error has the so called“solar cycle effect”,i.e.the error is large when solar activity is high,and small when the solar activity is low.In addition,the predicted values of F_10.7 are very close to the observed values,and the correlation coefficient between them reaches 0.98.Then we compare the prediction results of the LSTM model with those of the back propagation（BP）neural network model and the autoregressive（AR）model.It can be seen that the forecast errors of these three models are comparable for the 1-day forecast;but for the 2-or 3-day forecast,the performance of the LSTM model is significantly better than the other two models.Finally,we investigate the prediction’s leading time and find that the LSTM model can successfully predict the F_10.7 up to 51 days later with no significant increase in error.After that,this paper continues to apply the LSTM model to the prediction of SSN.The results show that good achievements are obtained in the forecasting of both daily and 13-month smoothed SSN.Particularly,the prediction of the 13-month smoothed SSN can keep its accuracy until the leading time reaches 46 months（the root mean square error ranging from 1.51 to 3.08）,which demonstrates that the LSTM model has the ability to predict the medium-term change of solar cycles.