# Probabilistic Solar Proxy Forecasting with Neural Network Ensembles

arXiv: https://arxiv.org/abs/2306.02169 · HTML: https://mlsanity.com/paper/2306.02169/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 3 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Local minima in training of neural networks](https://mlsanity.com/paper/1611.06310/) (2016)
- [Simultaneous Multivariate Forecast of Space Weather Indices using Deep Neural Network Ensembles](https://mlsanity.com/paper/2112.09051/) (2021)
- [Reduced Order Probabilistic Emulation for Physics-Based Thermosphere Models](https://mlsanity.com/paper/2211.04392/) (2022)

## Built on by (most cited first, 2 of 2)

- [Enhancing Solar Driver Forecasting with Multivariate Transformers](https://mlsanity.com/paper/2406.15847/) (2024)
- [Daily Predictions of F10.7 and F30 Solar Indices with Deep Learning](https://mlsanity.com/paper/2604.10045/) (2026)

## Abstract (arXiv)

Space weather indices are used commonly to drive forecasts of thermosphere density, which directly affects objects in low-Earth orbit (LEO) through atmospheric drag. One of the most commonly used space weather proxies, F10.7 cm, correlates well with solar extreme ultra-violet (EUV) energy deposition into the thermosphere. Currently, the USAF contracts Space Environment Technologies (SET), which uses a linear algorithm to forecast F10.7 cm. In this work, we introduce methods using neural network ensembles with multi-layer perceptrons (MLPs) and long-short term memory (LSTMs) to improve on the SET predictions. We make predictions only from historical F10.7 cm values, but also investigate data manipulation to improve forecasting. We investigate data manipulation methods (backwards averaging and lookback) as well as multi step and dynamic forecasting. This work shows an improvement over the baseline when using ensemble methods. The best models found in this work are ensemble approaches using multi step or a combination of multi step and dynamic predictions. Nearly all approaches offer an improvement, with the best models improving between 45 and 55% on relative MSE. Other relative error metrics were shown to improve greatly when ensembles methods were used. We were also able to leverage the ensemble approach to provide a distribution of predicted values; allowing an investigation into forecast uncertainty. Our work found models that produced less biased predictions at elevated and high solar activity levels. Uncertainty was also investigated through the use of a calibration error score metric (CES), our best ensemble reached similar CES as other work.