Graph-Augmented LSTM with Weighted Loss for Enhanced Energy Forecasting

Accurate energy consumption forecasting is critical for modern power systems, supporting both operational reliability and cost optimization. Deep learning approaches, particularly Long Short-Term Memory (LSTM) networks, have become increasingly prevalent in time-series load forecasting. However, typical LSTM-based solutions do not explicitly model interfeature correlations and often undervalue peak-load periods, which are crucial for grid stability and energy market operations. This paper proposes a Graph-Aug LSTM (Graph-Augmented LSTM) with a weighted loss function. First, we construct a feature-level correlation graph and employ a Graph Attention Network (GAT) to learn a global embedding that captures crossfeature relationships. This embedding is concatenated at each LSTM time step, providing the model with explicit awareness of inter-feature dependencies. As an additional novelty, we introduce a Weighted Mean Squared Error (MSE) that emphasizes peak consumption intervals, thereby reducing the risk of underestimating high-demand periods. Validation on multiple U.S. city datasets demonstrates that our approach consistently outperforms naive baselines, a standard LSTM, and XGBoost in both overall error metrics and peak-load accuracy. These results highlight the value of integrating graph-based feature embeddings with a peak-focused loss function for more reliable and interpretable load forecasting.