Symmetric Decomposition Framework for Enhanced Air Quality Prediction: A Component-Wise Linear Modeling Approach

Air quality prediction is a critical and complex time-series forecasting task, where traditional linear models often struggle to capture non-stationary, multiscale temporal dynamics. While recent advances in deep learning have improved predictive performance, challenges remain in interpretability, component disentanglement, and structured modeling. In this work, we propose a symmetric decomposition–modeling–evaluation framework tailored for air quality forecasting. Our method decomposes air quality time series into three complementary components: trend, periodicity, and fluctuation, based on their structural characteristics and symmetry relationships. Each component is modeled using lightweight, component-specific linear modules that preserve interpretability and computational efficiency. Importantly, the framework explicitly leverages the symmetrical properties between components to inform both model design and multiscale interaction. To evaluate component-level prediction quality, we introduce dual series-wise metrics that assess temporal correlation and distributional symmetry, addressing the limitations of conventional point-wise error metrics in capturing sequence-level consistency. Experimental results on real-world AQI datasets and other public time-series benchmarks demonstrate that our approach achieves competitive forecasting accuracy. On the Beijing dataset, our method achieved an MAE of 0.445 at the 96 h prediction horizon, outperforming the best baseline model, PatchFormer, with an MAE of 0.464. On the Tianjin dataset, our method achieved an MAE of 0.466 compared to the best competing model’s MAE of 0.481. Across multiple datasets, our approach consistently outperformed traditional methods, with improvements in MAE ranging from 0.019 to 0.086, demonstrating its effectiveness in capturing complex temporal patterns while enhancing interpretability through symmetry-aware modeling and evaluation.