PMGT-Net: A physics-informed multi-scale graph transformer framework for explainable national energy dependency forecasting
Yasin Ozkan
article (Uluslararası, Hakemli) | Yazar(lar): Yasin Ozkan | Yıl: 2026 | Dergi/Kurum: APPLIED ENERGY | İndeks: WOS.SCI | DOI: 10.1016/j.apenergy.2026.128724 | Anahtar Kelimeler: National energy dependency forecasting, Graph transformer networks, Energy forecasting, Time series forecasting, Deep learning for energy syste
Accurate forecasting of national energy dependency is critically important for sustainable energy planning, energy security, and strategic policy development. However, national energy systems exhibit highly complex temporal dynamics, interdependent energy relationships, and nonlinear consumption-import interactions, making reliable forecasting a challenging task. Existing forecasting approaches generally focus on temporal modeling while insufficiently capturing dynamic relational dependencies among multiple energy components. To address these limitations, this study proposes a Physics-Informed Multi-Scale Graph Transformer Network (PMGT-Net) framework for national energy dependency forecasting using monthly EMRA/EPDK energy data. The proposed framework integrates multi-scale temporal learning, dynamic graph construction, Graph Transformer-based relational modeling, and physics-informed optimization within a unified forecasting architecture. Unlike existing energy forecasting approaches that primarily emphasize temporal modeling or address graph learning, physics-informed optimization, and explainability as separate components, PMGT-Net jointly integrates these complementary mechanisms within a unified end-to-end framework specifically designed for national energy dependency forecasting. In addition, explainable artificial intelligence (XAI) mechanisms are incorporated to improve interpretability and analyze the contribution of individual energy variables to forecasting decisions. The framework models complex interactions among electricity, natural gas, petroleum, and LPG production-consumption-import variables while simultaneously learning long-term temporal dependencies and energy-balance constraints. Extensive experiments were conducted using comparative deep learning and Transformer-based baseline models, including LSTM, GRU, Bi-LSTM, Transformer, Informer, Autoformer, FED-former, PatchTST, iTransformer and ST-GNN architectures. Experimental results demonstrate that the proposed PMGT-Net framework achieves superior forecasting performance with lower RMSE, MAE, and MAPE values compared with all comparative models. Ablation analyses confirm the effectiveness of each architectural component, while robustness analyses demonstrate stable forecasting capability under noisy, missing-value, and seasonal-shift scenarios. Furthermore, statistical significance tests verify that the observed performance improvements are statistically meaningful. Explainability analyses reveal that natural gas imports, petroleum-related indicators, and electricity consumption are among the most influential variables affecting national energy dependency forecasting. Overall, the proposed PMGT-Net framework provides an effective, interpretable, and physically informed forecasting solution for national energy dependency analysis. The framework can support energy policy development, strategic energy planning, sustainable resource management, and decision-support systems for future smart energy infrastructures.