<p>Low Earth orbit satellites are potentially impacted by atmospheric drag due to short-term enhancements in thermospheric density induced by solar irradiance and solar wind disturbances, affecting the design of launch missions to the safe landing of spacecraft on Earth. We utilize hourly solar and geomagnetic indices and thermospheric density as measured by Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) satellites during the minimum and rising phases of solar activity from 2018 to 2022. Bidirectional Long Short-Term Memory (Bi-LSTM) and Gated Recurrent Unit (GRU) neural networks based on empirical mode decomposition (EMD) features are used to predict the thermospheric density. We found that the EMD of thermospheric density provided robust feature for the GRU and the Bi-LSTM models. The predictions are more effective in the rising phase when the thermospheric density is typically high which is of interested in satellite drags. The inputs of thermospheric density and its intrinsic mode functions (IMFs) with solar and geomagnetic indices improved prediction abilities for the rising phase, while only the IMFs of density or the geomagnetic indices is sufficient for the minimum phase. For categories based on disturbed and quiet geomagnetic conditions, the best prediction is for the coronal mass ejection (CME) event. The maximum values of <i>R</i>² is in the stream interaction region-high speed solar wind event for both Bi-LSTM and GRU models with correlation coefficients 0.914 and 0.922, respectively. The Bi-LSTM is more suitable for predicting the thermospheric density during "SpaceX storm" of consecutive CME-CME geomagnetic storms, while the temporal-dependent variations in the density are accurately predicted by the GRU model. Predictions by both deep learning models are more accurate than by the NRLMSIS 2.0 model. This study reveals the main physical mechanisms driving the short-term variations in the thermospheric density.</p>