Conformal Uncertainty Quantification Guarantees for Neural Operators

What the math gives to ML

The paper turns a functional prediction problem into a scalar split-conformal problem by scoring each residual field through its spatial quantile, rather than requiring simultaneous pointwise coverage everywhere. This is valuable for neural operators because it gives a calibrated statement about the fraction of a continuum or grid on which an entire predicted solution is accurate, while allowing heterogeneous spatial uncertainty through a scale field. The construction can be attached to FNO, DeepONet, or other operator surrogates without changing their training objective. The key experiment should test domain-fraction coverage and band tightness against max-residual and pointwise conformal baselines.