Post Constraint and Correction: A Plug-and-Play Module for Boosting the Performance of Deep Learning Based Weather Multivariate Time Series Forecasting

Weather forecasting is essential for various applications such as agriculture and transportation, and relies heavily on meteorological sequential data such as multivariate time series collected from weather stations. Traditional numerical weather prediction (NWP) methods applied to multivariate time series forecasting are grounded in statistical principles such as Autoregressive Integrated Moving Average (ARIMA); however, they often struggle with capturing complex nonlinear patterns among meteorological variables and temporal variances. Currently, existing deep learning approaches such as Recurrent Neural Networks (RNNs) and transformers offer remarkable performance in handling complex patterns among meteorological multivariate time series, yet frequently fail to maintain weather-specific physical properties such as strict values constraints, while also incurring the significant computational costs of large parameter scales. In this paper, we present a novel deep learning plug-and-play framework named Post Constraint and Correction (PCC) to address these challenges by incorporating additional constraints and corrections based on weather-specific properties such as multivariant correlations and physical-based strict value constraints into the prediction process. Our method demonstrates notable computational efficiency, delivering significant improvements over existing deep learning time series models and helping to achieve better performance with far fewer parameters. Extensive experiments demonstrate the effectiveness, efficiency, and robustness of our method, highlighting its potential for real-world applications.