Learn the Shape, Calibrate the Scale: Simulator-Trained Conformal Prediction under Sim-to-Real Shift

Conformal prediction provides finite-sample coverage guarantees, but adaptive intervals are difficult to deploy when labeled target data are scarce, even when a simulator can provide abundant synthetic data. We propose SUIT, a two-stage framework that learns the input-dependent uncertainty shape from the simulator and uses a small number of real samples to calibrate a scalar scale correction. This decomposition separates transferable uncertainty structure from the sim-to-real gap: zero-shot prediction is possible when the simulator is faithful, scalar calibration removes arbitrary global scale shifts, and stratification controls the residual spatial heterogeneity of the scale ratio. A conservative, computable audit of zero-shot degradation provides a stratum-wise lower bound on coverage from a small number of real audit points and flags inconclusive strata for recalibration. Experiments on distinct-value estimation, species-richness estimation, simulation-based inference, and synthetic regression show near-nominal zero-shot coverage under faithful simulation and coverage recovery with only 100 real samples under a 10× scale mismatch, at substantially narrower intervals than global conformal baselines.