Distribution-Free Uncertainty-Aware Virtual Sensing via Conformalized Neural Operators

TL;DR

The paper introduces CMCO, a distribution-free uncertainty quantification framework for neural operators that provides reliable, calibrated prediction intervals without retraining, enabling trustworthy real-time virtual sensing across diverse applications.

Contribution

It presents the Conformalized Monte Carlo Operator (CMCO), a novel method combining Monte Carlo dropout and conformal prediction within neural operators for distribution-free uncertainty quantification.

Findings

Achieves near-nominal coverage in diverse applications.

Provides spatially resolved uncertainty estimates without retraining.

Operates efficiently with minimal computational overhead.

Abstract

Robust uncertainty quantification (UQ) remains a critical barrier to the safe deployment of deep learning in real-time virtual sensing, particularly in high-stakes domains where sparse, noisy, or non-collocated sensor data are the norm. We introduce the Conformalized Monte Carlo Operator (CMCO), a framework that transforms neural operator-based virtual sensing with calibrated, distribution-free prediction intervals. By unifying Monte Carlo dropout with split conformal prediction in a single DeepONet architecture, CMCO achieves spatially resolved uncertainty estimates without retraining, ensembling, or custom loss design. Our method addresses a longstanding challenge: how to endow operator learning with efficient and reliable UQ across heterogeneous domains. Through rigorous evaluation on three distinct applications: turbulent flow, elastoplastic deformation, and global cosmic radiation dose estimation-CMCO consistently attains near-nominal empirical coverage, even in settings with strong spatial gradients and proxy-based sensing. This breakthrough offers a general-purpose, plug-and-play UQ solution for neural operators, unlocking real-time, trustworthy inference in digital twins, sensor fusion, and safety-critical monitoring. By bridging theory and deployment with minimal computational overhead, CMCO establishes a new foundation for scalable, generalizable, and uncertainty-aware scientific machine learning.