mlsanityData to 7 Oct 2026

Conformal Uncertainty Quantification Guarantees for Neural Operators

arXiv 2608.28515 ↗First posted 28 Aug 2026math.NA cs.AI cs.NAcited by 0

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Abstract (arXiv)

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∈(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 spaces, covering both continuum domains and fixed discretizations. Under mild assumptions on the data distribution, we show that the coverage conditional on the calibration set follows a Beta distribution, which we verify with numerical experiments on Darcy flow and Navier--Stokes equations, where our calibration yields bands consistently tighter than existing corrections while retaining the target coverage.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 38 of its 50 references that are in the map. First posted on arXiv 28 Aug 2026.

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38 of 50 references.

References · 38

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26 more
  1. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
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  22. 2025A Conformal Prediction Framework for Uncertainty Quantification in Physics-Informed Neural Networkscited by 5
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  25. 2024Structure-Preserving Operator Learningcited by 3
  26. 2026Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regimecited by 1

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