这篇论文提出了一种新的神经算子不确定性量化方法，在达西流和纳维-斯托克斯方程实验中表现优异。
研究人员开发了分割保形框架，为神经算子输出提供校准点带，确保在至少1-γ比例的评估域内包含真实解，置信度为1-α。该方法将归一化残差场降至空间(1-γ)分位数，并使用保留的校准数据集计算缩放因子。在达西流和纳维-斯托克斯方程的数值实验中，该方法校准产生的带状区域比现有校正方法更紧致，同时保持目标覆盖率。
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 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.