FROST: Stochastic Prediction-Space Adaptation for Sim-to-Real PDE Forecasting

Simulation pretraining followed by real-data fine-tuning is a natural strategy for adapting learned PDE forecasters, such as neural operators, to physical experiments. Yet deterministic adaptation can leave a structured mismatch between forecasts and experimental futures, whose variability reflects unresolved dynamics and measurement noise. To this end, we introduce FROST (Frozen-Operator Stochastic Transport), which freezes an upstream forecaster during correction and learns the conditional distribution of its residual from real measurements. Conditioned on observed history and the base forecast, FROST corrects systematic bias while modeling structured variability around the forecast. Across five RealPDEBench systems, FROST improves long-horizon ensemble-mean accuracy and fair CRPS over the corresponding fine-tuned FNO on every system, with reductions of up to 61% and 75%, respectively, and matches or outperforms every deterministic and generative baseline in mean rollout accuracy on all five systems. Additionally, we find that when applying FROST, the base FNO need not be fine-tuned at all. Together, these results establish stochastic prediction-space correction as a powerful complementary axis of sim-to-real adaptation for PDE forecasting.