Physics-constrained inverse neural estimation (PINE) of daily NOx emissions from TROPOMI NO₂ columns over the North China Plain

Abstract. Daily-resolution NOx emissions are pivotal for air-quality forecasting, yet static inventories cannot capture day-to-day variability, and conventional satellite inversions are either computationally prohibitive (4D-Var) or circularly dependent on pre-existing emission products. We introduce physics-constrained inverse neural estimation (PINE), instantiated for NOx as PINE-NOx, which retrieves daily NOx emissions over the North China Plain (0.1°, 364 days of 2023) from Sentinel-5P/TROPOMI NO₂ columns. PINE is a physics-constrained autoencoder: a neural encoder maps observed columns to emissions, which a fixed, differentiable transport–chemistry operator decodes back into columns. Physics thus enters structurally through this decoder, not as a soft residual penalty; trained end-to-end to reconstruct observations without emission labels. On 80 season-balanced validation days, PINE-NOx-inferred emissions raise the log-space spatial correlation between simulated and observed columns from 0.395 to 0.837 (Δr = +0.442, p < 0.001), robustly across four encoder backbones and all four seasons. Two independent checks corroborate the inversion: an independent WRF-Chem simulation cuts the summer column bias from +113 % to +5 %, and the recovered seasonal cycle agrees with the fully independent, bottom-up MEIC inventory (r = 0.68), while a prior-removal experiment confirms that the spatial pattern originates from the observations rather than the prior. The inventory provides the daily-resolved dynamics of North China Plain NOx emissions, a physically disaggregated emission winter/summer ratio of ~1.4, and ~11 % spatial redistribution relative to EDGAR. PINE-NOx offers a physically interpretable, label-free and computationally inexpensive paradigm for atmospheric emission inversion.