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

2025-07-15

AI Summary

Uncertainty quantification (UQ) in virtual sensing remains challenging under high-risk scenarios due to sparse, noisy, and non-collocated sensor data. Method: This paper proposes a distribution-free, real-time deployable neural operator UQ framework that integrates Monte Carlo Dropout and Split Conformal Prediction into the DeepONet architecture—without distributional assumptions, retraining, or model ensembling—enabling calibrated prediction intervals for spatially continuous physical fields. Contribution/Results: The approach is plug-and-play and significantly reduces computational overhead. Evaluated on three canonical physics tasks—turbulent flow modeling, elastoplastic deformation, and cosmic radiation dose estimation—the method achieves prediction interval coverage consistently near nominal levels (e.g., 90%), markedly enhancing the trustworthiness and robustness of deep learning in safety-critical applications.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Robust uncertainty quantification in deep learning virtual sensing
• Calibrated prediction intervals for neural operator-based sensing
• Efficient uncertainty-aware inference in heterogeneous scientific domains

Innovation

• Conformalized Monte Carlo Operator for neural operators
• Unifies Monte Carlo dropout with conformal prediction
• Provides distribution-free uncertainty quantification without retraining