Learning to Repair Physical Violations in Frozen Weather Foundation Models

Weather foundation models can achieve strong predictive accuracy while producing states that violate physically meaningful relationships. We study whether such violations can be repaired after forecasting, without modifying the forecasting model. ConserveFM learns an additive correction conditioned on a frozen forecast, the preceding atmospheric state, and forecast lead, and optimizes predictive fidelity together with moisture, hydrostatic, advection, and spectral consistency. We evaluate post-hoc repair on ERA5 under 60 matched stress conditions spanning three forecast leads, five structured corruption families, and four severities. An accuracy-oriented variant achieves the best stress NRMSE of $0.3008$ and ACC of $0.9503$. A physics-oriented variant reduces the aggregate physical-violation ratio from $0.852$ to $0.333$, while increasing stress NRMSE to $0.3159$. Direct state prediction occupies an intermediate Pareto-optimal regime. These results show that predictive accuracy and physical consistency are distinct objectives: stronger physical repair can be obtained without retraining the backbone, but not without a measurable predictive cost.