Operator models are regression algorithms between Banach spaces of functions. They have become an increasingly critical tool for spatiotemporal forecasting and physics emulation, especially in high-stakes scenarios where robust, calibrated uncertainty quantification is required. We introduce Local Sliced Conformal Inference (LSCI), a distribution-free framework for generating function-valued, locally adaptive prediction sets for operator models. We prove finite-sample validity and derive a data-dependent upper bound on the coverage gap under local exchangeability. On synthetic Gaussian-process tasks and real applications (air quality monitoring, energy demand forecasting, and weather prediction), LSCI yields tighter sets with stronger adaptivity compared to conformal baselines. We also empirically demonstrate robustness against biased predictions and certain out-of-distribution noise regimes.

翻译：算子模型是函数巴拿赫空间之间的回归算法。它们已成为时空预测和物理仿真的关键工具，尤其在需要稳健、校准的不确定性量化的高风险场景中。本文提出局部切片共形推断（LSCI），一种无需分布假设的框架，用于为算子模型生成函数值、局部自适应的预测集。我们证明了有限样本有效性，并在局部可交换性假设下推导了覆盖间隙的数据依赖上界。在合成高斯过程任务和实际应用（空气质量监测、能源需求预测和天气预测）中，与共形基线方法相比，LSCI能产生更紧凑且具有更强自适应性的预测集。我们还通过实证验证了该方法对偏倚预测和特定分布外噪声机制的鲁棒性。