Conformal Uncertainty Quantification Guarantees for Neural Operators
Neural operators provide fast surrogate models for approximating operators between function spaces, but their predictions often lack uncertainty quantification. We develop a split conformal framework to guarantee that a calibrated pointwise band around the neural operator output contains the true solution on at least a $1-γ$ fraction of the evaluation domain, with probability at least $1-α$ over test and calibration inputs, where $α,γ\in(0,1)$. Our method reduces a normalized residual field to its spatial $(1-γ)$-quantile and computes a scaling factor using a held-out calibration dataset. We prove marginal coverage guarantees for measurable residual fields defined on arbitrary probability...
| Authors | Tom Stent, Nicolas Boullé |
|---|---|
| Primary category | math.NA |
| Published | 28 August 2026 |
| Last updated at source | 28 August 2026 |
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