Sparse-Observation Atmospheric Thermal Forecasting with Physics-Informed Neural Networks for Climate-Aware Digital Twins

Summary

This paper evaluates a physics-informed neural network (PINN) for 1-3-hour forecasts of atmospheric potential temperature, constrained by a pressure-coordinate thermodynamic advection-source equation whose diabatic-source closure is fitted on the preceding 12 hours and frozen before future-time training. Using hourly ERA5 reanalysis at 700/850/925 hPa, the model is tested as a conditional hindcast against persistence, local-trend, a coordinate-only neural network, and a forcing-aware network receiving the same future meteorological forcing, plus a post-hoc best-of-baselines oracle envelope. In Oklahoma, mean RMSE improvement over the strongest baseline grows from 8.1% at +1 h to 23.8% at +3 h under dense observations; under nested 25/10/5% virtual observation networks the +3 h advantage remains 14.6-16.9%. A fixed-protocol transfer to an Alabama heat event yields 19.7-24.4% improvement at +3 h across three observation layouts. A Montana terrain stress test degrades by roughly 17.5% at +3 h, exposing the fixed pressure-level representation as an applicability limit. Strengths include the forcing-matched baseline isolating the physics constraint, frozen closure limiting leakage, and the honest negative result. Main limitations: evaluation uses withheld ERA5 values as virtual observations, future meteorological forcing is still supplied (not operational), each region contributes only four forecast origins with descriptive statistics, and the Montana test confounds terrain with a collapsed sensor pool. Code is publicly available.