Electroencephalographic (EEG) signals play a crucial role in neuroscience research and clinical diagnostics, particularly in sleep monitoring and the prevention of acute health events such as apnea and epileptic seizures. However, traditional predictive models often struggle with the inherent nonlinear complexity, boundary effects, and high computational demands of EEG data, limiting their accuracy and real-time applicability. To address these challenges, we propose a novel hybrid decomposition-ensemble framework integrating a Mapping Neural Network (MNN) and Long Short-Term Memory (LSTM). MNN learns the intrinsic mapping between raw EEG signals and their decomposed components, enhancing feature representation and mitigating boundary effects, achieving an average coefficient of determination \((R^2)\) of 0.952 in predictive performance. Additionally, a partial decomposition strategy retains only the high-frequency components most relevant to short-term forecasting, effectively reducing computational complexity. Compared to state-of-the-art methods, our approach exhibits superior accuracy and robustness in short-term forecasting, providing a reliable solution for real-time sleep monitoring.