Climate Temporal Temperature Prediction via an Interpretable Kolmogorov–Arnold Neural Network

Accurate temperatures 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 Temp<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-KAN. Grounded in the Kolmogorov-Arnold representation theorem, Temp<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-KAN explores to replace conventional linear weights in neural network 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 train Temp<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-KAN to map historical trends to multi-horizon forecasts. Rigorous evaluations on real-world climate datasets demonstrate Temp<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-KAN’s dual advantage achieving state-of-the-art prediction accuracy (reducing RMSE by 14.7% vs. MLPs) while utilizing 63% fewer trainable parameters. In addition, a systematic ablation study quantifies the sensitivity of key Temp<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-KAN-specific hyperparameters (spline order <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>, grid resolution <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">grid</i>) on forecasting performance. Finally, we theoretically prove Temp<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-KAN’s universal approximation capacity through function space analysis, and practically, we demonstrate its interpretability by visualizing learned activation patterns that correlate with known climate drivers. These innovations position Temp<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-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 enhance its viability for operational forecasting systems. The code is available at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/YongxiangLei/TempKAN</i>.