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

Area of Science:

• Climate Informatics
• Artificial Intelligence
• Meteorology

Background:

• Accurate temperature forecasting is crucial for weather informatics and climate monitoring.
• Traditional models often lack interpretability and struggle with complex nonlinear climate patterns.
• Deep learning offers potential but frequently results in 'black-box' models.

Purpose of the Study:

• Introduce Tem²-KAN, a novel deep learning architecture for high-precision climate temperature forecasting.
• Replace conventional neural network weights with spline-parameterized univariate functions for dynamic learning.
• Integrate universal approximation with physically meaningful feature visualization for interpretable climate models.

Main Methods:

• Developed Tem²-KAN based on the Kolmogorov-Arnold representation theorem.
• Implemented a pipeline involving meteorological data preprocessing and Tem²-KAN training.
• Conducted rigorous evaluations and ablation studies on real-world UK climate datasets.

Main Results:

• Tem²-KAN achieved state-of-the-art prediction accuracy in temperature forecasting.
• The model demonstrated superior performance using fewer trainable parameters compared to existing methods.
• Ablation studies quantified the impact of hyperparameters like spline order and grid resolution.

Conclusions:

• Tem²-KAN offers a paradigm shift in climate informatics, providing both high predictive performance and mechanistic insight.
• The framework's reduced hyperparameter complexity enhances its suitability for operational forecasting.
• Theoretical and practical demonstrations confirm Tem²-KAN's universal approximation capacity, interpretability, and prediction performance.