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：算子模型是巴拿赫函数空间之间的回归算法。它们已成为时空预测和物理仿真中日益关键的工具，特别是在需要稳健、校准的不确定性量化等高风险的场景中。我们提出了局部切片共形推断（LSCI），这是一种无分布框架，用于为算子模型生成函数值形式的、局部自适应的预测集。我们证明了有限样本的有效性，并在局部可交换性条件下推导出覆盖间隙的数据相关上界。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报）中，与共形基线方法相比，LSCI 产生了更紧凑且具有更强自适应性的预测集。我们还通过实验证明，该方法对偏差预测和某些分布外噪声场景具有稳健性。