# KARMAN: Benchmarking thermospheric density estimation

## Team

• Giacomo Acciarini (University of Surrey)
• Edward Brown (University of Cambridge)
• Stefano Bonasera (UC Boulder)
• Jorge A. Pérez-Hernández (Mexico National Autonomous University)
• Bernard Benson (University of Alabama Huntsville)
• Eric Sutton (UC Boulder)
• Moriba K. Jah (University of Texas, Austin)
• Christopher Bridges (University of Surrey)
• Atılım Güneş Baydin (University of Oxford)

## Abstract

Accurately estimating spacecraft location is of crucial importance for a variety of safety-critical tasks in low-Earth orbit (LEO), including satellite collision avoidance and re-entry. The solar activity largely impacts the physical characteristics of the thermosphere, consequently affecting the trajectories of spacecraft in LEO. Stateof-the-art models for estimating thermospheric ensity are either computationally expensive or under-perform during extreme solar activity. Moreover, these models provide single-point solutions, neglecting critical information on the associated uncertainty. In this work we use and compare two methods, Monte Carlo dropout and deep ensembles, to estimate thermospheric total mass density and associated uncertainty. The networks are trained using ground-truth density data from five wellcalibrated satellites, using orbital data information, solar and geomagnetic indices as input. The trained models improve for a subset of atellites upon operational solutions, also providing a measure of uncertainty in the density estimation.

## Publications

1. Bonasera, Stefano, Giacomo Acciarini, Jorge A. Pérez-Hernández, Bernard Benson, Edward Brown, Eric Sutton, Moriba K. Jah, Christopher Bridges, and Atılım Güneş Baydin. 2021. “Dropout and Ensemble Networks for Thermospheric Density Uncertainty Estimation.” In Bayesian Deep Learning Workshop, NeurIPS 2021.

Accurately estimating spacecraft location is of crucial importance for a variety of safety-critical tasks in low-Earth orbit (LEO), including satellite collision avoidance and re-entry. The solar activity largely impacts the physical characteristics of the thermosphere, consequently affecting the trajectories of spacecraft in LEO. Stateof-the-art models for estimating thermospheric density are either computationally expensive or under-perform during extreme solar activity. Moreover, these models provide single-point solutions, neglecting critical information on the associated uncertainty. In this work we use and compare two methods, Monte Carlo dropout and deep ensembles, to estimate thermospheric total mass density and associated uncertainty. The networks are trained using ground-truth density data from five wellcalibrated satellites, using orbital data information, solar and geomagnetic indices as input. The trained models improve for a subset of satellites upon operational solutions, also providing a measure of uncertainty in the density estimation.

@inproceedings{bonasera-2021-ensemble,
title = {Dropout and Ensemble Networks for Thermospheric Density Uncertainty Estimation},
author = {Bonasera, Stefano and Acciarini, Giacomo and {Pérez-Hernández}, Jorge A. and Benson, Bernard and Brown, Edward and Sutton, Eric and Jah, Moriba K. and Bridges, Christopher and Baydin, {Atılım Güneş}},
booktitle = {Bayesian Deep Learning workshop, {NeurIPS} 2021},
year = {2021}
}

2. Brown, Edward, Stefano Bonasera, Bernard Benson, Jorge A. Pérez-Hernández, Giacomo Acciarini, Atılım Güneş Baydin, Christopher Bridges, Meng Jin, Eric Sutton, and Moriba K. Jah. 2021. “Learning the Solar Latent Space: Sigma-Variational Autoencoders for Multiple Channel Solar Imaging.” In Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021).

This study uses a sigma-variational autoencoder to learn a latent space of solar images using the 12 channels taken by Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI) instruments on-board the NASA Solar Dynamics Observatory. The model is able to significantly compress the large image dataset to 0.19% of its original size while still proficiently reconstructing the original images. As a downstream task making use of the learned representation, this study demonstrates the of use the learned latent space as an input to improve the forecasts of the F30 solar radio flux index, compared to an off-the-shelf pretrained ResNet feature extractor. Finally, the developed models can be used to generate realistic synthetic solar images by sampling from the learned latent space.

@inproceedings{brown-2021-learning,
title = {Learning the solar latent space: sigma-variational autoencoders for multiple channel solar imaging},
author = {Brown, Edward and Bonasera, Stefano and Benson, Bernard and {Pérez-Hernández}, Jorge A. and Acciarini, Giacomo and Baydin, {Atılım Güneş} and Bridges, Christopher and Jin, Meng and Sutton, Eric and Jah, Moriba K.},
booktitle = {Fourth Workshop on Machine Learning and the Physical Sciences ({NeurIPS} 2021)},
year = {2021}
}

3. Benson, Bernard, Edward Brown, Stefano Bonasera, Giacomo Acciarini, Jorge A. Pérez-Hernández, Eric Sutton, Moriba K. Jah, Christopher Bridges, Meng Jin, and Atılım Güneş Baydin. 2021. “Simultaneous Multivariate Forecast of Space Weather Indices Using Deep Neural Network Ensembles.” In Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021).

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 shortterm 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.

@inproceedings{benson-2021-simultaneous,
title = {Simultaneous Multivariate Forecast of Space Weather Indices using Deep Neural Network Ensembles},
author = {Benson, Bernard and Brown, Edward and Bonasera, Stefano and Acciarini, Giacomo and {Pérez-Hernández}, Jorge A. and Sutton, Eric and Jah, Moriba K. and Bridges, Christopher and Jin, Meng and Baydin, {Atılım Güneş}},
booktitle = {Fourth Workshop on Machine Learning and the Physical Sciences ({NeurIPS} 2021)},
year = {2021}
}


## Acknowledgments

This work has been enabled by the Frontier Development Lab (FDL.ai). FDL is a co-operative agreement between NASA, the SETI Institute (seti.org), and Trillium Technologies Inc, in partnership with Google Cloud and Intel. We would like to thank Drs. L. Guhathakurta, M. Jin, J. van den Ijssel, E. Doornbos, A. Muñoz-Jaramillo, A. Vourlidas, I. Telezhinsky, and T.S. Kelso for sharing their technical expertise and James Parr, Jodie Hughes, and Belina Raffy for their support.