Heterogeneous Graph Kolmogorov–Arnold Networks for Spatio-Temporal Wind Power Forecasting

Accurate short-term wind power forecasting is critical for reliable grid operation, efficient reserve management, and large-scale renewable energy integration, yet turbine-level prediction in utility-scale wind farms remains challenging due to complex wake interactions, heterogeneous spatial dependencies, and highly nonlinear temporal dynamics. To address these challenges, this paper proposes a Heterogeneous Graph Kolmogorov–Arnold Network (HG-KAN), a novel functional message-passing framework that jointly models multiple complementary relational structures within a unified heterogeneous graph. The proposed model incorporates three distinct edge types spatial proximity, directional wake influence, and empirical power correlation each represented through learnable univariate function approximators inspired by the Kolmogorov–Arnold representation theorem, enabling relation-specific nonlinear message functions that better align with turbine physics than conventional linear graph neural network transformations. HG-KAN is evaluated on a real-world utility-scale wind farm dataset comprising 200 turbines, three meteorological masts, and 8,764 hourly observations, where it consistently exceeds homogeneous and single-relation graph baselines. The best configuration, combining spatial and wake-based relations with five KAN basis functions, the optimized HG-KAN configuration achieves an R² of 0.3991 (compared to 0.2981 for the vanilla configuration), surpassing the strongest baseline ST-GAT (R² = 0.3906) with statistical significance (p < 0.05). Ablation studies confirm that wake-aware relational modeling and functional edge transformations are the primary drivers of performance gains, while multi-horizon forecasting results demonstrate equal or superior accuracy, particularly in short-term horizons (1–3 h), without sacrificing interpretability. Overall, the proposed HG-KAN framework highlights the importance of physics-informed heterogeneous relational learning and functional message passing for accurate spatio-temporal wind power forecasting and offers a promising direction for other complex energy systems.