Tem²-KAN: Data-driven temporal temperature prediction via an improved Kolmogorov-Arnold network

Accurate temperature forecasting relies on traditional meteorological parameters that are essential for monitoring weather informatics and guiding forecasting efforts. This study introduces a deep learning architecture for high-precision climate temperature forecasting via an improved Kolmogorov-Arnold Networks, named Tem²-KAN. Grounded in the Kolmogorov-Arnold representation theorem, Tem²-KAN explores replacing conventional linear weights in neural networks with spline-parameterized univariate functions, enabling dynamic learning of nonlinear climate patterns while maintaining intrinsic interpretability. The proposed framework uniquely integrates the universal approximation capabilities of Multi-Layer Perceptrons (MLPs) with physically meaningful feature visualization through its adaptive activation functions, addressing critical limitations of black-box climate models. A temperature prediction pipeline is established that first preprocesses raw meteorological data from UK monitoring stations, then trains Tem²-KAN to map historical trends to multi-horizon forecasts. Rigorous evaluations on real-world climate datasets demonstrate Tem²-KAN's dual advantage achieving state-of-the-art prediction accuracy while utilizing fewer trainable parameters. In addition, a systematic ablation study quantifies the sensitivity of key Tem²-KAN-specific hyperparameters (spline order k, grid resolution grid) on forecasting performance. Finally, we theoretically prove Tem²-KAN's universal approximation capacity through function space analysis, and practically, we demonstrate its interpretability and prediction performance. These innovations position Tem²-KAN as a paradigm-shifting tool for climate informatics, offering meteorologists both high predictive performance and mechanistic insight into temperature dynamics. The framework's reduced hyperparameter complexity further enhances its viability for operational forecasting systems.