A Machine Learning-Based Thermospheric Density Model with Uncertainty Quantification

Conventional thermospheric density models are limited in their ability to capture solar-geomagnetic coupling dynamics and lack probabilistic uncertainty estimates. We present MSIS-UN (NRLMSISE-00 with Uncertainty Quantification), an innovative framework integrating sparse principal component analysis (sPCA) with heteroscedastic neural networks. Our methodology leverages multi-satellite density measurements from the CHAMP, GRACE, and SWARM missions, coupled with MSIS-00-derived exospheric temperature (tinf) data. The technical approach features three key innovations: (1) spherical harmonic decomposition of T∞ using spatiotemporally orthogonal basis functions, (2) sPCA-based extraction of dominant modes from sparse orbital sampling data, and (3) neural network prediction of temporal coefficients with built-in uncertainty quantification. This integrated framework significantly enhances the temperature calculation module in MSIS-00 while providing probabilistic density estimates. Validation against SWARM-C measurements demonstrates superior performance, reducing mean absolute error (MAE) during quiet periods from MSIS-00’s 44.1% to 23.7%, with uncertainty bounds (1σ) achieving an MAE of 8.4%. The model’s dynamic confidence intervals enable rigorous probabilistic risk assessment for LEO satellite collision avoidance systems, representing a paradigm shift from deterministic to probabilistic modeling of thermospheric density.