Mon Oct 13, F. Flechtner
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Li, Ling, He, Changyong, Zheng, Dunyong, Li, Shaoning, and Zhao, Dong, 2025. A Prior Knowledge-Enhanced Deep Learning Framework for Improved Thermospheric Mass Density Prediction. Atmosphere, 16(5):539, doi:10.3390/atmos16050539.
• from the NASA Astrophysics Data System • by the DOI System •
@ARTICLE{2025Atmos..16..539L,
author = {{Li}, Ling and {He}, Changyong and {Zheng}, Dunyong and {Li}, Shaoning and {Zhao}, Dong},
title = "{A Prior Knowledge-Enhanced Deep Learning Framework for Improved Thermospheric Mass Density Prediction}",
journal = {Atmosphere},
keywords = {thermospheric mass density prediction, ResNet, deep learning, prior knowledge, NRLMSIS-2.1},
year = 2025,
month = may,
volume = {16},
number = {5},
eid = {539},
pages = {539},
abstract = "{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 {\texttimes} <inline-formula><mml:math><mml:semantics><mm
l:mrow><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mr
ow><mml:mo>‑</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:msup></
mml:mrow></mml:semantics></mml:math></inline-formula> kg/m$^{3}$
in TMD prediction compared with 0.2750 {\texttimes} <inline-form
ula><mml:math><mml:semantics><mml:mrow><mml:msup><mml:mrow><mml:
mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>‑</mml:mo><mml:mn>12<
/mml:mn></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:m
ath></inline-formula> kg/m$^{3}$ 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{\textendash}2009, altitude of
305{\textendash}505 km, avg. 376 km) under quiet geomagnetic
conditions (Kp {\ensuremath{\leq}} 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{\textendash}2009, altitude of 450{\textendash}540 km, avg.
482 km) under magnetically quiet conditions, with the RMSE
decreasing from 0.3352 {\texttimes} <inline-formula><mml:math><m
ml:semantics><mml:mrow><mml:msup><mml:mrow><mml:mn>10</mml:mn></
mml:mrow><mml:mrow><mml:mo>‑</mml:mo><mml:mn>12</mml:mn></mml:mr
ow></mml:msup></mml:mrow></mml:semantics></mml:math></inline-
formula> kg/m$^{3}$ to 0.2959 {\texttimes} <inline-formula><mml:
math><mml:semantics><mml:mrow><mml:msup><mml:mrow><mml:mn>10</mm
l:mn></mml:mrow><mml:mrow><mml:mo>‑</mml:mo><mml:mn>12</mml:mn><
/mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></inl
ine-formula> kg/m$^{3}$, 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.}",
doi = {10.3390/atmos16050539},
adsurl = {https://ui.adsabs.harvard.edu/abs/2025Atmos..16..539L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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