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Abstract

With rapid development of artificial intelligence technology, machine learning has been widely applied to the thermospheric mass density (TMD) modeling. In this study we propose a machine-learning approach, the bidirectional gated recurrent unit with multi-head attention mechanism (BGMA), for modeling and predicting the TMD, based on the Gravity Recovery and Climate Experiment (GRACE) satellite data. GRACE data spanning over one solar cycle provide a valuable opportunity to explore altitude and solar activity dependencies in TMD. We selected 11 key parameters to construct the model, the correlation coefficient (R2) between the model's predictions and satellite observations is 0.944, significantly outperforming the 0.893 of the latest version of the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Extended Model (NRLMSIS-2.0). In addition, the TMD measurements from GRACE Follow-On satellite served as an independent test to evaluate the BGMA model's generalization, yielding an R2 of 0.924, underscoring the model's robustness. A critical aspect of our work is minimizing the number of input parameters while maintaining high prediction accuracy. And the interpretability analysis of the input parameters using the Shapley additive explanation algorithm has been applied, revealing that the altitude, solar activity index P10.7 and solar zenith angle are the three most influential parameters affecting TMD variations at GRACE satellite. When using just these three parameters, the R2 still reaches 0.842. Additionally, our model demonstrated robust performance over varying prediction durations, with R2 exceeding 0.800 for predictions extending up to 1 hr. These results highlight the BGMA model's effectiveness in accurately predicting TMD.