The Dependence of the Sunspot Forecast Accuracy Using LSTM Networks From Number of Cycles in the Training Set

Abstract

In this paper the forecast of the sunspot time series with Long Short-Term Memory (LSTM) artificial neural network is presented. The research is mainly focused on the experimental estimation of dependence between accuracy of the forecast and the number of solar cycles in the training set of the learning procedure of LSTM-network. The two main approaches to the forecast are presented: single-step forecast by monthly correction with known observations, and multi-step forecast in a closed-loop form of autoregressive sequence. The test forecast batch is represented by the modern 24th cycle of solar activity (between 2008 and 2019 years), while the training set changes up to 22 previous solar cycles. The presented results show that there is no evident dependence between number of previous cycles in the training set and the forecast accuracy. The single-step forecast is more accurate than the multi-step scheme for the mid-term and long-term forecasts (up to 10 times). The overall prediction of sunspot time series is possible and requires at least more than 6 cycles in the training set, but does not provide any significant increase in accuracy (below 2%) against modern known formal forecast methods of monthly sunspot numbers. The refinement of LSTM sequence is required for better results.