Air-IFF-PINN: an Air-Pollution Inverse-Forward Fourier Physics-Informed Neural Network framework for reconstructing...

Satellite-derived air pollution datasets often contain missing values caused by retrieval limitations, cloud cover, and uneven spatial-temporal coverage. This article presents Air-IFF-PINN, an Air-Pollution Inverse-Forward Fourier Physics-Informed Neural Network framework for reconstructing and imputing incomplete pollutant fields when key physical parameters are unknown. The method combines an advection-diffusion formulation, a multi-mode Fourier feature PINN architecture, and a staged inverse-forward training strategy. In the inverse stage, the effective diffusion parameter is estimated from incomplete observations. In the forward stage, the estimated parameter is used to reconstruct missing satellite-derived pollutant values within the observed spatial-temporal domain. The workflow is demonstrated using Sentinel-5P/TROPOMI Level-3 carbon monoxide data and ERA5-Land wind fields over the Jakarta Metropolitan Area during a major fire event. The method provides a reproducible framework for handling incomplete satellite observations, estimating unknown PDE parameters, and generating physically coherent pollutant reconstructions within the observed spatial-temporal domain.