Conformal Uncertainty Quantification Guarantees for Neural Operators

arXiv:2608.28515v1 Announce Type: cross Abstract: 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 $1-\gamma$ fraction of the evaluation domain, with probability at least $1-\alpha$ over test and calibration inputs, where $\alpha,\gamma\in(0,1)$. Our method reduces a normalized residual field to its spatial $(1-\gamma)$-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.

Abstract: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 $1-\gamma$ fraction of the evaluation domain, with probability at least $1-\alpha$ over test and calibration inputs, where $\alpha,\gamma\in(0,1)$. Our method reduces a normalized residual field to its spatial $(1-\gamma)$-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.

Numerical Analysis (math.NA); Artificial Intelligence (cs.AI); Probability (math.PR)

arXiv:2608.28515 [math.NA]

(or arXiv:2608.28515v1 [math.NA] for this version)

https://doi.org/10.48550/arXiv.2608.28515 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

Conformal Uncertainty Quantification Guarantees for Neural Operators

Related coverage