Short‑horizon atmospheric temperature forecasts are essential for climate‑aware digital‑twin systems, yet observations are often incomplete. This work evaluates a physics‑informed neural network (PINN) for potential‑temperature prediction. The network is constrained by the thermodynamic advection‑source equation in pressure coordinates and uses a diabatic‑source closure fitted from the preceding 12‑hour window, which is then frozen during future‑time training. Hourly ERA5 reanalysis at three pressure levels serves as input, and the model is tested as a conditional hindcast at lead times of one, two, and three hours against persistence, local‑trend, and two neural‑network baselines; one baseline receives the same future meteorological forcing as the PINN to isolate the effect of the physical constraint.
In an Oklahoma development case, mean RMSE improvement over the strongest baseline grew from 8.1% at one hour to 23.8% at three hours. When observation density was reduced to 5% of candidate sites, the three‑hour advantage remained between 14.6% and 16.9%, with no sign that lower density improves performance. Applying the same protocol to an Alabama heat‑wave event with three virtual‑observation layouts yielded three‑hour improvements of 19.7%‑24.4%, consistently winning at the original level.
A parallel stress test in Montana, where fixed pressure levels intersected complex terrain, produced a degradation of roughly 17.5% at three hours, highlighting a terrain‑related limit of the fixed vertical‑coordinate formulation. Overall, the physics constraint’s benefit increases with forecast horizon, persists under severe observation sparsity, and transfers across regions, but is bounded by the validity of a fixed vertical coordinate over complex terrain. This insight is relevant to physics‑constrained components of climate‑aware forecasting and digital‑twin systems.
Review