$\text{CO}_{2}$-Net: A Physics-Informed Spatio-Temporal Model for Global Surface $\text{CO}_{{2}}$ Reconstruction

Reconstructing atmospheric surface CO 2 is crucial for understanding climate dynamics and informing global mitigation strategies. Traditional inversion models achieve precise global CO 2 reconstruction but rely heavily on uncertain prior estimates of fluxes and emissions. Inspired by recent advances in data-driven weather forecasting, we explore whether data-driven models can reduce reliance on these priors. However, CO 2 reconstruction presents unique challenges, including complex spatio-temporal dynamics, periodic patterns and sparse observations. We propose CO 2 -Net, a data-driven model that addresses these challenges without requiring extensive prior data. We formulate CO 2 reconstruction as solving a constrained advection-diffusion equation and derive three key components: physics-informed spatio-temporal factorization for capturing complex transport dynamics, wind-based embeddings for modeling periodic variations and a semi-supervised loss for integrating sparse CO 2 observations with dense meteorological data. CO 2 -Net is designed in three sizes-small (S), base (B) and large (L)-to balance performance and efficiency. On CMIP6 reanalysis data, CO 2 -Net (S) and (L) reduce RMSE by 11% and 71%, respectively, when compared to the best data-driven baseline. On real observations, CO 2 -Net (L) achieves RMSE comparable to inversion models. The ablation study shows that the effectiveness of wind-based embedding and semi-supervised loss stems from their compatibility with our spatio-temporal factorization. Code is available at https://github.com/Leamonz/CORE.