Physics-Guided Dual Neural ODEs with Bidirectional Information Exchange for Air Quality Prediction

Air pollution, a critical issue tied to urban life, is governed by complex physical processes that make accurate air quality prediction highly challenging. Recent physics-guided neural networks attempt to address this by modeling physical and data-driven branches independently and fusing their representations at the end. However, these approaches often suffer from error accumulation within each branch and difficulties in the effective fusion of representations. To address these problems, we propose \textbf{LIMBO} (\textbf{L}inkage \textbf{I}nter\textbf{M}ediaries \textbf{B}etween neural \textbf{O}rdinary differential equations), a physics-guided neural network augmented with an information exchange mechanism. LIMBO introduces bidirectional information exchange between the physical and data-driven branches and employs a dedicated LIMBO loss function to mitigate error accumulation and enhance collaboration. We further examine the effect of different exchange intervals on model performance and validate the contribution of the loss function through ablation studies. Experimental results show that LIMBO outperforms the state-of-the-art Air-DualODE model in PM2.5 forecasting, underscoring its practical value for real-world urban air quality prediction. The code is available at \href{https://github.com/jiaxu-feng/LIMBO}{https://github.com/jiaxu-feng/LIMBO}.