# Machine-Learned HASDM Model with Uncertainty Quantification

arXiv: https://arxiv.org/abs/2109.07651 · HTML: https://mlsanity.com/paper/2109.07651/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 48 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 2 of 2)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Meaningful uncertainties from deep neural network surrogates of large-scale numerical simulations](https://mlsanity.com/paper/2010.13749/) (2020)

## Built on by (most cited first, 1 of 1)

- [Uncertainty Quantification Techniques for Space Weather Modeling: Thermospheric Density Application](https://mlsanity.com/paper/2201.02067/) (2022)

## Abstract (arXiv)

The first thermospheric neutral mass density model with robust and reliable uncertainty estimates is developed based on the SET HASDM density database. This database, created by Space Environment Technologies (SET), contains 20 years of outputs from the U.S. Space Force's High Accuracy Satellite Drag Model (HASDM), which represents the state-of-the-art for density and drag modeling. We utilize principal component analysis (PCA) for dimensionality reduction, creating the coefficients upon which nonlinear machine-learned (ML) regression models are trained. These models use three unique loss functions: mean square error (MSE), negative logarithm of predictive density (NLPD), and continuous ranked probability score (CRPS). Three input sets are also tested, showing improved performance when introducing time histories for geomagnetic indices. These models leverage Monte Carlo (MC) dropout to provide uncertainty estimates, and the use of the NLPD loss function results in well-calibrated uncertainty estimates without sacrificing model accuracy (<10% mean absolute error). By comparing the best HASDM-ML model to the HASDM database along satellite orbits, we found that the model provides robust and reliable uncertainties in the density space over all space weather conditions. A storm-time comparison shows that HASDM-ML also supplies meaningful uncertainty measurements during extreme events.