Locally Adaptive Conformal Inference for Operator Models

Abstract: Operator models are regression algorithms for functional data and have become a key tool for emulating large-scale dynamical systems. Recent advances in deep neural operators have dramatically improved the accuracy and scalability of operator modeling, but lack an inherent notion of predictive uncertainty. We introduce Local Spectral Conformal Inference (LSCI), a new framework for locally adaptive, distribution-free uncertainty quantification for neural operator models. LSCI uses projection-based depth scoring and localized conformal inference to generate function-valued prediction sets with statistical guarantees. We prove approximate finite-sample marginal coverage under local exchangeability, and demonstrate significant gains in adaptivity and coverage across synthetic and real-world operator learning tasks.