Technical Article

BaLNet: A probabilistic Bayesian neural network for solar wind speed forecasting

¹ Department of Computer Engineering, Space Weather Research Group, University of Alcalá, Plaza San Diego s/n, 28801 Alcalá de Henares, Madrid, Spain
² Department of Physics and Mathematics, Space Weather Research Group, University of Alcalá, Plaza San Diego s/n, 28801 Alcalá de Henares, Madrid, Spain

^* Corresponding author: mario.cobos@uah.es

Received: 31 October 2024
Accepted: 30 June 2025

Abstract

Machine Learning has gained favor as a tool for space weather event forecasting over the last few years. In the context of solar wind forecasting, efforts have been primarily focused on forecasting the bulk speed of solar wind. Although steps have been taken in improving the accuracy of forecasts, a common concern from an operational point of view has been determining the reliability of any given prediction. In this work, we present BaLNet, a variational neural network with a normal probability distribution output as a tool for providing operational forecasts of solar wind speed with uncertainty quantification. For a lead time of five days, we find reductions in root mean squared error between 38% and 55%, depending on the test set, when compared to state-of-the-art neural networks. Similarly, for the same lead time, we obtain a correlation coefficient between prediction and observation of 0.89 to 0.94, compared to the correlation coefficient of 0.15 obtained by state-of-the-art models. Cross-validation results confirm robust generalization across temporal variations, maintaining consistent superiority over baseline methods. We also leverage the properties of the Bayesian inference process supporting the resulting model to estimate the degree and sources of uncertainty for any given forecast. We provide 95% confidence interval for each prediction computed from the standard deviation of the forecasted normal distribution. For a lead time of five days, BaLNet’s prediction interval coverage probability is of 95% in the test set, evidencing that the target conditional probability distribution is being succesfully extracted. The method presented allows for a full training of the model to converge in a span of 2.17 h in CPU. This process can be further accelerated by using a GPU to reduce the training time to an average of 15 min.