A Novel Pi-Style Dendritic Neural Network Based on Kolmogorov-Arnold Representation for Time Series Modeling

Abstract

Time series forecasting is essential across domains such as energy, finance, and climate, yet conventional statistical and deep learning methods often struggle to balance accuracy, efficiency, and interpretability when modeling complex, nonlinear temporal patterns. This study introduces the Pi-style Dendritic Kolmogorov-Arnold Network (PiDKAN), a novel hybrid neural architecture that integrates the multiplicative structure of Pi-Sigma networks, the localized processing of Dendritic Neural Models, and the univariate function decomposition capability of Kolmogorov-Arnold Networks. By capturing both local and high-order interactions, PiDKAN addresses key challenges in time series modeling. The model was benchmarked against ten established neural networks using eight electricity consumption datasets spanning four years, consistently achieving superior performance in RMSE, MAE, and MAPE metrics. Statistical analyses confirmed the significance of these improvements, demonstrating PiDKAN's strength as a robust, and accurate forecasting solution. These results suggest that PiDKAN offers a promising new direction for interpretable time series models in real-world applications.