[论文] Conformal Uncertainty Quantification Guarantees for Neural Operators

论文概要

研究领域: ML 作者: Tom Stent, Nicolas Boullé 发布时间: 2026-08-28 arXiv: 2608.28515

中文摘要

神经算子为近似函数空间之间的算子提供了快速的替代模型，但它们的预测通常缺乏不确定性量化。我们开发了一个分裂保形框架，以保证校准的逐点带围绕神经算子输出包含至少1-γ比例的评估域上的真实解，概率至少为1-α，其中α,γ∈(0,1)。我们的方法将归一化残差场约简为其空间(1-γ)-分位数，并使用留出校准数据集计算缩放因子。我们在任意概率空间上定义的可测残差场的边际覆盖保证，涵盖连续域和固定离散化。在数据分布的温和假设下，我们表明给定校准集的覆盖遵循Beta分布，这我们通过Darcy流和Navier-Stokes方程的数值实验进行了验证，其中我们的校准产生了始终比现有校正更紧的带，同时保持目标覆盖。

原文摘要

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 ...

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