  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.
