Physics-informed Machine Learning to Constrain Anthropogenic SO$_2$ Emission

Satellite-based and inventory-based sulfur dioxide emissions estimates persistently disagree, compounding uncertainty in aerosol radiative forcing. We present a physics-informed neural network, PIM-Plume, that infers point-source sulfur dioxide emissions from satellite column density measurements by predicting a ventilation coefficient, which combines with plume mass through a fixed physical relationship rather than unconstrained regression. Trained on 13 South Korean emitter clusters and evaluated across synthetic noise tiers, PIM-Plume achieves $R^2=0.84$ under low noise and $R^2=0.48$ at GEMS-realistic noise, outperforming an end-to-end baseline throughout. Results indicate that instrument sensitivity remains the binding constraint on operational satellite-based emission monitoring.