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.