[Paper Review] Simultaneous Multivariate Forecast of Space Weather Indices using Deep Neural Network Ensembles

Bernard Benson, Edward Brown+8 more|arXiv (Cornell University)|Dec 16, 2021

Solar and Space Plasma Dynamics4 citations

TL;DR

This paper proposes a deep learning ensemble model using long short-term memory (LSTM) networks to simultaneously forecast multiple space weather indices—solar radio flux and geomagnetic indices—over a 27-day horizon. By integrating both time series data and solar image inputs, the model achieves a 30–40% reduction in root mean square error compared to time series-only baselines, demonstrating improved accuracy and uncertainty quantification via model ensembling.

ABSTRACT

Solar radio flux along with geomagnetic indices are important indicators of solar activity and its effects. Extreme solar events such as flares and geomagnetic storms can negatively affect the space environment including satellites in low-Earth orbit. Therefore, forecasting these space weather indices is of great importance in space operations and science. In this study, we propose a model based on long short-term memory neural networks to learn the distribution of time series data with the capability to provide a simultaneous multivariate 27-day forecast of the space weather indices using time series as well as solar image data. We show a 30-40\% improvement of the root mean-square error while including solar image data with time series data compared to using time series data alone. Simple baselines such as a persistence and running average forecasts are also compared with the trained deep neural network models. We also quantify the uncertainty in our prediction using a model ensemble.

Motivation & Objective

• To improve the accuracy of simultaneous multivariate forecasts of space weather indices, including solar radio flux and geomagnetic indices.
• To integrate solar image data with time series data to enhance predictive performance beyond traditional time-series-only models.
• To quantify predictive uncertainty using an ensemble of deep neural networks.
• To outperform simple baselines such as persistence and running average forecasts in multivariate space weather prediction.
• To support space operations and scientific understanding by enabling reliable 27-day forecasts of solar activity impacts.

Proposed method

• Employs a deep neural network architecture based on long short-term memory (LSTM) networks to model temporal dependencies in multivariate time series data.
• Combines sequential time series data of space weather indices with spatial solar image data from solar observatories as input features.
• Trains an ensemble of multiple LSTM models to improve robustness and enable uncertainty quantification in predictions.
• Uses a 27-day forecasting horizon to align with the solar rotation period, improving forecast relevance for space weather applications.
• Applies standard loss functions and training procedures for sequence-to-sequence prediction, with model averaging for final forecasts.
• Evaluates performance using root mean square error (RMSE) and compares results against persistence and running average baselines.

Experimental results

Research questions

• RQ1 Can the integration of solar image data with time series data significantly improve the accuracy of multivariate space weather forecasts?
• RQ2 How does the performance of the proposed LSTM ensemble model compare to simple baseline forecasting methods like persistence and running average?
• RQ3 To what extent does model ensembling improve uncertainty quantification in space weather predictions?
• RQ4 Does the inclusion of solar image data lead to a measurable reduction in forecast error for key indices like solar radio flux and geomagnetic indices?
• RQ5 Can a single deep learning model effectively forecast multiple space weather indices simultaneously over a 27-day horizon?

Key findings

• The inclusion of solar image data with time series data reduced the root mean square error (RMSE) by 30–40% compared to models using time series data alone.
• The proposed deep neural network ensemble model outperformed both the persistence and running average baseline models in terms of RMSE across all forecasted indices.
• Model ensembling enabled reliable quantification of predictive uncertainty, enhancing confidence in forecast reliability.
• The model achieved simultaneous multivariate forecasting of solar radio flux and geomagnetic indices over a 27-day horizon, aligning with the solar rotation period.
• The results demonstrate that deep learning models incorporating multimodal data (time series and images) are highly effective for complex space weather prediction tasks.
• The study confirms that solar image data provides valuable spatiotemporal information that enhances forecasting beyond what time series alone can offer.