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Machine learning (ML) has often been applied to space weather (SW) problemsin recent years. SW originates from solar perturbations and is comprised of theresulting complex variations they cause within the systems between the Sun andEarth. These systems are tightly coupled and not well understood. This createsa need for skillful models with knowledge about the confidence of theirpredictions. One example of such a dynamical system is the thermosphere, theneutral region of Earth's upper atmosphere. Our inability to forecast it hassevere repercussions in the context of satellite drag and collision avoidanceoperations for objects in low Earth orbit. Even with (assumed) perfect driverforecasts, our incomplete knowledge of the system results in often inaccurateneutral mass density predictions. Continuing efforts are being made to improvemodel accuracy, but density models rarely provide estimates of uncertainty. Inthis work, we propose two techniques to develop nonlinear ML models to predictthermospheric density while providing calibrated uncertainty estimates: MonteCarlo (MC) dropout and direct prediction of the probability distribution, bothusing the negative logarithm of predictive density (NLPD) loss function. Weshow the performance for models trained on local and global datasets. Thisshows that NLPD provides similar results for both techniques but the directprobability method has a much lower computational cost. For the global modelregressed on the SET HASDM density database, we achieve errors of 11% onindependent test data with well-calibrated uncertainty estimates. Using anin-situ CHAMP density dataset, both techniques provide test error on the orderof 13%. The CHAMP models (on independent data) are within 2% of perfectcalibration for all prediction intervals tested. This model can also be used toobtain global predictions with uncertainties at a given epoch.

Uncertainty Quantification Techniques for Space Weather Modeling: Thermospheric Density Application