$\text{CO}_2$-Net: A Physics-Informed Spatio-Temporal Model for Global $\text{CO}_2$ Reconstruction

Reconstructing atmospheric (\text{CO}_2) is essential for understanding climate dynamics and supporting global climate mitigation strategies. Traditional inversion methods is able to reconstruct atmospheric CO2 by integrating sparse (\text{CO}_2) observations with auxiliary meteorological variables in transport models but are computationally intensive and largely depend on uncertain priors. While deep neural networks have made significant advancements in weather forecasting, data-driven approaches for global (\text{CO}_2) reconstruction remain unexplored. (\text{CO}_2) reconstruction presents unique challenges including spatio-temporal dynamics, periodic patterns, and sparse observations rarely encountered in conventional tasks. We propose (\text{CO}_2)-Net, a deep learning framework addressing these challenges to achieve inversion-level accuracy without extensive prior data. Framed as a constrained advection-diffusion equation, we theoretically derive three components: physics-informed spatio-temporal factorization, wind-based embeddings, and a semi-supervised loss. Based on CarbonTracker and CMIP6 datasets, (\text{CO}_2)-Net reduces bias by up to 70\% compared to the conventional deep neural networks. At GLOBALVIEWplus observation spots, it well replicates observed variability with a RMSE matching inversion models. Further ablation studies are performed to validate the effectiveness of each component, which indicates a practical application of deep neural network in the global data reconstruction.