A Prior Knowledge-Enhanced Deep Learning Framework for Improved Thermospheric Mass Density Prediction

Accurate thermospheric mass density (TMD) prediction is critical for applications in solar-terrestrial physics, spacecraft safety, and remote sensing systems. While existing deep learning (DL)-based TMD models are predominantly data-driven, their performance remains constrained by observational data limitations. This study proposes ResNet-MSIS, a novel hybrid framework that integrates prior knowledge from the empirical NRLMSIS-2.1 model into a residual network (ResNet) architecture. The incorporation of NRLMSIS-2.1 enhanced the performance of ResNet-MSIS, yielding a lower root mean squared error (RMSE) of 0.2657 × kg/m³ in TMD prediction compared with 0.2750 × kg/m³ from ResNet, along with faster convergence during training and better generalization on Gravity Recovery and Climate Experiment (GRACE-A) data, which was trained and validated on the CHAllenging Minisatellite Payload (CHAMP) TMD data (2000–2009, altitude of 305–505 km, avg. 376 km) under quiet geomagnetic conditions (Kp ≤ 3). The DL model was subsequently tested on the remaining CHAMP-derived TMD observations, and the results demonstrated that ResNet-MSIS outperformed both ResNet and NRLMSIS-2.1 on the test dataset. The model’s robustness was further demonstrated on GRACE-A data (2002–2009, altitude of 450–540 km, avg. 482 km) under magnetically quiet conditions, with the RMSE decreasing from 0.3352 × kg/m³ to 0.2959 × kg/m³, indicating improved high-altitude prediction accuracy. Additionally, ResNet-MSIS effectively captured the horizontal TMD variations, including equatorial mass density anomaly (EMA) and midnight density maximum (MDM) structures, confirming its ability to learn complex spatiotemporal patterns. This work underscores the value of merging data-driven methods with domain-specific prior knowledge, offering a promising pathway for advancing TMD modeling in space weather and atmospheric research.